%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : MGT025-1 : TPTP v9.3.0. Released v2.4.0.
% Transfm : NO INFORMATION
% Format : NO INFORMATION
% Command : run_E %s %d THM
% Computer : n013.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 8 06:24:00 AM UTC 2026
% Result : Unsatisfiable 0.12s 0.40s
% Output : Proof 0.22s
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : MGT025-1 : TPTP v9.3.0. Released v2.4.0.
% 0.00/0.03 % Command : run_E %s %d THM
% 0.07/0.34 % Computer : n013.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Mon Sep 7 12:10:52 UTC 2026
% 0.07/0.34 % CPUTime :
% 0.12/0.40 % SZS status Unsatisfiable
% 0.12/0.40 % SZS output start Proof
% 0.12/0.40 tff(greater_type, type, (
% 0.12/0.40 greater: ( $i * $i ) > $o)).
% 0.12/0.40 tff(growth_rate_type, type, (
% 0.12/0.40 growth_rate: ( $i * $i ) > $i)).
% 0.12/0.40 tff(sk2_type, type, (
% 0.12/0.40 sk2: $i)).
% 0.12/0.40 tff(first_movers_type, type, (
% 0.12/0.40 first_movers: $i)).
% 0.12/0.40 tff(zero_type, type, (
% 0.12/0.40 zero: $i)).
% 0.12/0.40 tff(decreases_type, type, (
% 0.12/0.40 decreases: $i > $o)).
% 0.12/0.40 tff(cardinality_at_time_type, type, (
% 0.12/0.40 cardinality_at_time: ( $i * $i ) > $i)).
% 0.12/0.40 tff(efficient_producers_type, type, (
% 0.12/0.40 efficient_producers: $i)).
% 0.12/0.40 tff(increases_type, type, (
% 0.12/0.40 increases: $i > $o)).
% 0.12/0.40 tff(constant_type, type, (
% 0.12/0.40 constant: $i > $o)).
% 0.12/0.40 tff(sum_type, type, (
% 0.12/0.40 sum: ( $i * $i ) > $i)).
% 0.12/0.40 tff(number_of_organizations_type, type, (
% 0.12/0.40 number_of_organizations: ( $i * $i ) > $i)).
% 0.12/0.40 tff(sk1_type, type, (
% 0.12/0.40 sk1: $i)).
% 0.12/0.40 tff(subpopulation_type, type, (
% 0.12/0.40 subpopulation: ( $i * $i * $i ) > $o)).
% 0.12/0.40 tff(in_environment_type, type, (
% 0.12/0.40 in_environment: ( $i * $i ) > $o)).
% 0.12/0.40 tff(subpopulations_type, type, (
% 0.12/0.40 subpopulations: ( $i * $i * $i * $i ) > $o)).
% 0.12/0.40 tff(environment_type, type, (
% 0.12/0.40 environment: $i > $o)).
% 0.12/0.40 tff(1,assumption,(~increases(cardinality_at_time(first_movers, sk2))), introduced(assumption)).
% 0.12/0.40 tff(2,assumption,(~decreases(cardinality_at_time(first_movers, sk2))), introduced(assumption)).
% 0.12/0.40 tff(3,plain,
% 0.12/0.40 (subpopulations(first_movers, efficient_producers, sk1, sk2) <=> subpopulations(first_movers, efficient_producers, sk1, sk2)),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(4,axiom,(subpopulations(first_movers, efficient_producers, sk1, sk2)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_l7_48')).
% 0.12/0.40 tff(5,plain,
% 0.12/0.40 (subpopulations(first_movers, efficient_producers, sk1, sk2)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[4, 3])).
% 0.12/0.40 tff(6,plain,
% 0.12/0.40 (environment(sk1) <=> environment(sk1)),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(7,axiom,(environment(sk1)), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_l7_47')).
% 0.12/0.40 tff(8,plain,
% 0.12/0.40 (environment(sk1)),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[7, 6])).
% 0.12/0.40 tff(9,plain,
% 0.12/0.40 (^[B: $i, A: $i] : refl(((~environment(A)) | in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B))) <=> ((~environment(A)) | in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(10,plain,
% 0.12/0.40 (![B: $i, A: $i] : ((~environment(A)) | in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B))) <=> ![B: $i, A: $i] : ((~environment(A)) | in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[9])).
% 0.12/0.40 tff(11,plain,
% 0.12/0.40 (![B: $i, A: $i] : ((~environment(A)) | in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B))) <=> ![B: $i, A: $i] : ((~environment(A)) | in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.12/0.40 inference(rewrite,[status(thm)],[])).
% 0.12/0.40 tff(12,plain,
% 0.12/0.40 (^[B: $i, A: $i] : rewrite((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | in_environment(A, B)) <=> ((~environment(A)) | in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B))))),
% 0.12/0.40 inference(bind,[status(th)],[])).
% 0.12/0.40 tff(13,plain,
% 0.12/0.40 (![B: $i, A: $i] : (((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | in_environment(A, B)) <=> ![B: $i, A: $i] : ((~environment(A)) | in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.12/0.40 inference(quant_intro,[status(thm)],[12])).
% 0.12/0.40 tff(14,axiom,(![B: $i, A: $i] : (((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | in_environment(A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_time_point_occur_45')).
% 0.12/0.40 tff(15,plain,
% 0.12/0.40 (![B: $i, A: $i] : ((~environment(A)) | in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.12/0.40 inference(modus_ponens,[status(thm)],[14, 13])).
% 0.12/0.40 tff(16,plain,
% 0.12/0.40 (![B: $i, A: $i] : ((~environment(A)) | in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[15, 11])).
% 0.12/0.41 tff(17,plain,(
% 0.12/0.41 ![B: $i, A: $i] : ((~environment(A)) | in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.12/0.41 inference(skolemize,[status(sab)],[16])).
% 0.12/0.41 tff(18,plain,
% 0.12/0.41 (![B: $i, A: $i] : ((~environment(A)) | in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[17, 10])).
% 0.12/0.41 tff(19,plain,
% 0.12/0.41 (((~![B: $i, A: $i] : ((~environment(A)) | in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B)))) | ((~environment(sk1)) | in_environment(sk1, sk2) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)))) <=> ((~![B: $i, A: $i] : ((~environment(A)) | in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B)))) | (~environment(sk1)) | in_environment(sk1, sk2) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(20,plain,
% 0.12/0.41 ((~![B: $i, A: $i] : ((~environment(A)) | in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B)))) | ((~environment(sk1)) | in_environment(sk1, sk2) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(21,plain,
% 0.12/0.41 ((~![B: $i, A: $i] : ((~environment(A)) | in_environment(A, B) | (~subpopulations(first_movers, efficient_producers, A, B)))) | (~environment(sk1)) | in_environment(sk1, sk2) | (~subpopulations(first_movers, efficient_producers, sk1, sk2))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[20, 19])).
% 0.12/0.41 tff(22,plain,
% 0.12/0.41 (in_environment(sk1, sk2)),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[21, 18, 8, 5])).
% 0.12/0.41 tff(23,plain,
% 0.12/0.41 (^[B: $i, A: $i] : refl(((~in_environment(A, B)) | (~environment(A)) | subpopulation(first_movers, A, B)) <=> ((~in_environment(A, B)) | (~environment(A)) | subpopulation(first_movers, A, B)))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(24,plain,
% 0.12/0.41 (![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(first_movers, A, B)) <=> ![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(first_movers, A, B))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[23])).
% 0.12/0.41 tff(25,plain,
% 0.12/0.41 (![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(first_movers, A, B)) <=> ![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(first_movers, A, B))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(26,plain,
% 0.12/0.41 (^[B: $i, A: $i] : rewrite((((~environment(A)) | (~in_environment(A, B))) | subpopulation(first_movers, A, B)) <=> ((~in_environment(A, B)) | (~environment(A)) | subpopulation(first_movers, A, B)))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(27,plain,
% 0.12/0.41 (![B: $i, A: $i] : (((~environment(A)) | (~in_environment(A, B))) | subpopulation(first_movers, A, B)) <=> ![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(first_movers, A, B))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[26])).
% 0.12/0.41 tff(28,axiom,(![B: $i, A: $i] : (((~environment(A)) | (~in_environment(A, B))) | subpopulation(first_movers, A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_subpopulations_30')).
% 0.12/0.41 tff(29,plain,
% 0.12/0.41 (![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(first_movers, A, B))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[28, 27])).
% 0.12/0.41 tff(30,plain,
% 0.12/0.41 (![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(first_movers, A, B))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[29, 25])).
% 0.12/0.41 tff(31,plain,(
% 0.12/0.41 ![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(first_movers, A, B))),
% 0.12/0.41 inference(skolemize,[status(sab)],[30])).
% 0.12/0.41 tff(32,plain,
% 0.12/0.41 (![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(first_movers, A, B))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[31, 24])).
% 0.12/0.41 tff(33,plain,
% 0.12/0.41 (((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(first_movers, A, B))) | ((~environment(sk1)) | subpopulation(first_movers, sk1, sk2) | (~in_environment(sk1, sk2)))) <=> ((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(first_movers, A, B))) | (~environment(sk1)) | subpopulation(first_movers, sk1, sk2) | (~in_environment(sk1, sk2)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(34,plain,
% 0.12/0.41 (((~in_environment(sk1, sk2)) | (~environment(sk1)) | subpopulation(first_movers, sk1, sk2)) <=> ((~environment(sk1)) | subpopulation(first_movers, sk1, sk2) | (~in_environment(sk1, sk2)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(35,plain,
% 0.12/0.41 (((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(first_movers, A, B))) | ((~in_environment(sk1, sk2)) | (~environment(sk1)) | subpopulation(first_movers, sk1, sk2))) <=> ((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(first_movers, A, B))) | ((~environment(sk1)) | subpopulation(first_movers, sk1, sk2) | (~in_environment(sk1, sk2))))),
% 0.12/0.41 inference(monotonicity,[status(thm)],[34])).
% 0.12/0.41 tff(36,plain,
% 0.12/0.41 (((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(first_movers, A, B))) | ((~in_environment(sk1, sk2)) | (~environment(sk1)) | subpopulation(first_movers, sk1, sk2))) <=> ((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(first_movers, A, B))) | (~environment(sk1)) | subpopulation(first_movers, sk1, sk2) | (~in_environment(sk1, sk2)))),
% 0.12/0.41 inference(transitivity,[status(thm)],[35, 33])).
% 0.12/0.41 tff(37,plain,
% 0.12/0.41 ((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(first_movers, A, B))) | ((~in_environment(sk1, sk2)) | (~environment(sk1)) | subpopulation(first_movers, sk1, sk2))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(38,plain,
% 0.12/0.41 ((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(first_movers, A, B))) | (~environment(sk1)) | subpopulation(first_movers, sk1, sk2) | (~in_environment(sk1, sk2))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[37, 36])).
% 0.12/0.41 tff(39,plain,
% 0.12/0.41 (subpopulation(first_movers, sk1, sk2)),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[38, 32, 8, 22])).
% 0.12/0.41 tff(40,plain,
% 0.12/0.41 (^[A: $i, C: $i] : refl(((number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C))) | (~environment(A)) | (~subpopulation(first_movers, A, C))) <=> ((number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C))) | (~environment(A)) | (~subpopulation(first_movers, A, C))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(41,plain,
% 0.12/0.41 (![A: $i, C: $i] : ((number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C))) | (~environment(A)) | (~subpopulation(first_movers, A, C))) <=> ![A: $i, C: $i] : ((number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C))) | (~environment(A)) | (~subpopulation(first_movers, A, C)))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[40])).
% 0.12/0.41 tff(42,plain,
% 0.12/0.41 (![A: $i, C: $i] : ((number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C))) | (~environment(A)) | (~subpopulation(first_movers, A, C))) <=> ![A: $i, C: $i] : ((number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C))) | (~environment(A)) | (~subpopulation(first_movers, A, C)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(43,plain,
% 0.12/0.41 (^[A: $i, C: $i] : rewrite(((number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C))) | (~subpopulation(first_movers, A, C)) | (~environment(A))) <=> ((number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C))) | (~environment(A)) | (~subpopulation(first_movers, A, C))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(44,plain,
% 0.12/0.41 (![A: $i, C: $i] : ((number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C))) | (~subpopulation(first_movers, A, C)) | (~environment(A))) <=> ![A: $i, C: $i] : ((number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C))) | (~environment(A)) | (~subpopulation(first_movers, A, C)))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[43])).
% 0.12/0.41 tff(45,plain,
% 0.12/0.41 (![B: $i, A: $i, C: $i] : ((number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C))) | (~subpopulation(first_movers, A, C)) | (~environment(A))) <=> ![A: $i, C: $i] : ((number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C))) | (~subpopulation(first_movers, A, C)) | (~environment(A)))),
% 0.12/0.41 inference(elim_unused_vars,[status(thm)],[])).
% 0.12/0.41 tff(46,plain,
% 0.12/0.41 (![B: $i, A: $i, C: $i] : ((number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C))) | (~subpopulation(B, A, C)) | (~environment(A)) | (~(B = first_movers))) <=> ![B: $i, A: $i, C: $i] : ((number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C))) | (~subpopulation(first_movers, A, C)) | (~environment(A)))),
% 0.12/0.41 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.12/0.41 tff(47,plain,
% 0.12/0.41 (![B: $i, A: $i, C: $i] : ((number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C))) | (~subpopulation(B, A, C)) | (~environment(A)) | (~(B = first_movers))) <=> ![A: $i, C: $i] : ((number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C))) | (~subpopulation(first_movers, A, C)) | (~environment(A)))),
% 0.12/0.41 inference(transitivity,[status(thm)],[46, 45])).
% 0.12/0.41 tff(48,plain,
% 0.12/0.41 (![B: $i, A: $i, C: $i] : ((number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C))) | (~subpopulation(B, A, C)) | (~environment(A)) | (~(B = first_movers))) <=> ![A: $i, C: $i] : ((number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C))) | (~environment(A)) | (~subpopulation(first_movers, A, C)))),
% 0.12/0.41 inference(transitivity,[status(thm)],[47, 44])).
% 0.12/0.41 tff(49,plain,
% 0.12/0.41 (^[B: $i, A: $i, C: $i] : trans(monotonicity(rewrite((((~environment(A)) | (~subpopulation(B, A, C))) | (~(B = first_movers))) <=> ((~subpopulation(B, A, C)) | (~environment(A)) | (~(B = first_movers)))), (((((~environment(A)) | (~subpopulation(B, A, C))) | (~(B = first_movers))) | (number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C)))) <=> (((~subpopulation(B, A, C)) | (~environment(A)) | (~(B = first_movers))) | (number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C)))))), rewrite((((~subpopulation(B, A, C)) | (~environment(A)) | (~(B = first_movers))) | (number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C)))) <=> ((number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C))) | (~subpopulation(B, A, C)) | (~environment(A)) | (~(B = first_movers)))), (((((~environment(A)) | (~subpopulation(B, A, C))) | (~(B = first_movers))) | (number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C)))) <=> ((number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C))) | (~subpopulation(B, A, C)) | (~environment(A)) | (~(B = first_movers)))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(50,plain,
% 0.12/0.41 (![B: $i, A: $i, C: $i] : ((((~environment(A)) | (~subpopulation(B, A, C))) | (~(B = first_movers))) | (number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C)))) <=> ![B: $i, A: $i, C: $i] : ((number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C))) | (~subpopulation(B, A, C)) | (~environment(A)) | (~(B = first_movers)))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[49])).
% 0.12/0.41 tff(51,plain,
% 0.12/0.41 (![B: $i, A: $i, C: $i] : ((((~environment(A)) | (~subpopulation(B, A, C))) | (~(B = first_movers))) | (number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C)))) <=> ![A: $i, C: $i] : ((number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C))) | (~environment(A)) | (~subpopulation(first_movers, A, C)))),
% 0.12/0.41 inference(transitivity,[status(thm)],[50, 48])).
% 0.12/0.41 tff(52,axiom,(![B: $i, A: $i, C: $i] : ((((~environment(A)) | (~subpopulation(B, A, C))) | (~(B = first_movers))) | (number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C))))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_only_members_29')).
% 0.12/0.41 tff(53,plain,
% 0.12/0.41 (![A: $i, C: $i] : ((number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C))) | (~environment(A)) | (~subpopulation(first_movers, A, C)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[52, 51])).
% 0.12/0.41 tff(54,plain,
% 0.12/0.41 (![A: $i, C: $i] : ((number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C))) | (~environment(A)) | (~subpopulation(first_movers, A, C)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[53, 42])).
% 0.12/0.41 tff(55,plain,(
% 0.12/0.41 ![A: $i, C: $i] : ((number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C))) | (~environment(A)) | (~subpopulation(first_movers, A, C)))),
% 0.12/0.41 inference(skolemize,[status(sab)],[54])).
% 0.12/0.41 tff(56,plain,
% 0.12/0.41 (![A: $i, C: $i] : ((number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C))) | (~environment(A)) | (~subpopulation(first_movers, A, C)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[55, 41])).
% 0.12/0.41 tff(57,plain,
% 0.12/0.41 (((~![A: $i, C: $i] : ((number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C))) | (~environment(A)) | (~subpopulation(first_movers, A, C)))) | ((number_of_organizations(sk1, sk2) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))) | (~environment(sk1)) | (~subpopulation(first_movers, sk1, sk2)))) <=> ((~![A: $i, C: $i] : ((number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C))) | (~environment(A)) | (~subpopulation(first_movers, A, C)))) | (number_of_organizations(sk1, sk2) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))) | (~environment(sk1)) | (~subpopulation(first_movers, sk1, sk2)))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(58,plain,
% 0.12/0.41 ((~![A: $i, C: $i] : ((number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C))) | (~environment(A)) | (~subpopulation(first_movers, A, C)))) | ((number_of_organizations(sk1, sk2) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))) | (~environment(sk1)) | (~subpopulation(first_movers, sk1, sk2)))),
% 0.12/0.41 inference(quant_inst,[status(thm)],[])).
% 0.12/0.41 tff(59,plain,
% 0.12/0.41 ((~![A: $i, C: $i] : ((number_of_organizations(A, C) = sum(cardinality_at_time(first_movers, C), cardinality_at_time(efficient_producers, C))) | (~environment(A)) | (~subpopulation(first_movers, A, C)))) | (number_of_organizations(sk1, sk2) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))) | (~environment(sk1)) | (~subpopulation(first_movers, sk1, sk2))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[58, 57])).
% 0.12/0.41 tff(60,plain,
% 0.12/0.41 ((number_of_organizations(sk1, sk2) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))) | (~subpopulation(first_movers, sk1, sk2))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[59, 56, 8])).
% 0.12/0.41 tff(61,plain,
% 0.12/0.41 (number_of_organizations(sk1, sk2) = sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))),
% 0.12/0.41 inference(unit_resolution,[status(thm)],[60, 39])).
% 0.12/0.41 tff(62,plain,
% 0.12/0.41 (sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)) = number_of_organizations(sk1, sk2)),
% 0.12/0.41 inference(symmetry,[status(thm)],[61])).
% 0.12/0.41 tff(63,plain,
% 0.12/0.41 (constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))) <=> constant(number_of_organizations(sk1, sk2))),
% 0.12/0.41 inference(monotonicity,[status(thm)],[62])).
% 0.12/0.41 tff(64,plain,
% 0.12/0.41 (constant(number_of_organizations(sk1, sk2)) <=> constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))),
% 0.12/0.41 inference(symmetry,[status(thm)],[63])).
% 0.12/0.41 tff(65,plain,
% 0.12/0.41 (constant(number_of_organizations(sk1, sk2)) <=> constant(number_of_organizations(sk1, sk2))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(66,axiom,(constant(number_of_organizations(sk1, sk2))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_l7_49')).
% 0.12/0.41 tff(67,plain,
% 0.12/0.41 (constant(number_of_organizations(sk1, sk2))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[66, 65])).
% 0.12/0.41 tff(68,plain,
% 0.12/0.41 (constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))),
% 0.12/0.41 inference(modus_ponens,[status(thm)],[67, 64])).
% 0.12/0.41 tff(69,plain,
% 0.12/0.41 (^[B: $i, C: $i] : refl((constant(C) | decreases(B) | increases(B) | (~constant(sum(B, C)))) <=> (constant(C) | decreases(B) | increases(B) | (~constant(sum(B, C)))))),
% 0.12/0.41 inference(bind,[status(th)],[])).
% 0.12/0.41 tff(70,plain,
% 0.12/0.41 (![B: $i, C: $i] : (constant(C) | decreases(B) | increases(B) | (~constant(sum(B, C)))) <=> ![B: $i, C: $i] : (constant(C) | decreases(B) | increases(B) | (~constant(sum(B, C))))),
% 0.12/0.41 inference(quant_intro,[status(thm)],[69])).
% 0.12/0.41 tff(71,plain,
% 0.12/0.41 (![B: $i, C: $i] : (constant(C) | decreases(B) | increases(B) | (~constant(sum(B, C)))) <=> ![B: $i, C: $i] : (constant(C) | decreases(B) | increases(B) | (~constant(sum(B, C))))),
% 0.12/0.41 inference(rewrite,[status(thm)],[])).
% 0.12/0.41 tff(72,plain,
% 0.12/0.41 (![B: $i, A: $i, C: $i] : (constant(C) | decreases(B) | increases(B) | (~constant(sum(B, C)))) <=> ![B: $i, C: $i] : (constant(C) | decreases(B) | increases(B) | (~constant(sum(B, C))))),
% 0.12/0.41 inference(elim_unused_vars,[status(thm)],[])).
% 0.12/0.41 tff(73,plain,
% 0.12/0.41 (![B: $i, A: $i, C: $i] : (decreases(B) | increases(B) | (~constant(A)) | (~(A = sum(B, C))) | constant(C)) <=> ![B: $i, A: $i, C: $i] : (constant(C) | decreases(B) | increases(B) | (~constant(sum(B, C))))),
% 0.12/0.41 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.12/0.41 tff(74,plain,
% 0.12/0.41 (![B: $i, A: $i, C: $i] : (decreases(B) | increases(B) | (~constant(A)) | (~(A = sum(B, C))) | constant(C)) <=> ![B: $i, C: $i] : (constant(C) | decreases(B) | increases(B) | (~constant(sum(B, C))))),
% 0.12/0.41 inference(transitivity,[status(thm)],[73, 72])).
% 0.12/0.41 tff(75,plain,
% 0.12/0.41 (^[B: $i, A: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~(A = sum(B, C))) | (~constant(A))) <=> ((~constant(A)) | (~(A = sum(B, C))))), ((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) <=> (((~constant(A)) | (~(A = sum(B, C)))) | constant(C)))), rewrite((((~constant(A)) | (~(A = sum(B, C)))) | constant(C)) <=> ((~constant(A)) | (~(A = sum(B, C))) | constant(C))), ((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) <=> ((~constant(A)) | (~(A = sum(B, C))) | constant(C)))), (((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) | increases(B)) <=> (((~constant(A)) | (~(A = sum(B, C))) | constant(C)) | increases(B)))), rewrite((((~constant(A)) | (~(A = sum(B, C))) | constant(C)) | increases(B)) <=> (increases(B) | (~constant(A)) | (~(A = sum(B, C))) | constant(C))), (((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) | increases(B)) <=> (increases(B) | (~constant(A)) | (~(A = sum(B, C))) | constant(C)))), ((((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) | increases(B)) | decreases(B)) <=> ((increases(B) | (~constant(A)) | (~(A = sum(B, C))) | constant(C)) | decreases(B)))), rewrite(((increases(B) | (~constant(A)) | (~(A = sum(B, C))) | constant(C)) | decreases(B)) <=> (decreases(B) | increases(B) | (~constant(A)) | (~(A = sum(B, C))) | constant(C))), ((((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) | increases(B)) | decreases(B)) <=> (decreases(B) | increases(B) | (~constant(A)) | (~(A = sum(B, C))) | constant(C))))),
% 0.12/0.42 inference(bind,[status(th)],[])).
% 0.12/0.42 tff(76,plain,
% 0.12/0.42 (![B: $i, A: $i, C: $i] : (((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) | increases(B)) | decreases(B)) <=> ![B: $i, A: $i, C: $i] : (decreases(B) | increases(B) | (~constant(A)) | (~(A = sum(B, C))) | constant(C))),
% 0.12/0.42 inference(quant_intro,[status(thm)],[75])).
% 0.12/0.42 tff(77,plain,
% 0.12/0.42 (![B: $i, A: $i, C: $i] : (((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) | increases(B)) | decreases(B)) <=> ![B: $i, C: $i] : (constant(C) | decreases(B) | increases(B) | (~constant(sum(B, C))))),
% 0.12/0.42 inference(transitivity,[status(thm)],[76, 74])).
% 0.12/0.42 tff(78,axiom,(![B: $i, A: $i, C: $i] : (((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) | increases(B)) | decreases(B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_abc_sum_increase_36')).
% 0.12/0.42 tff(79,plain,
% 0.12/0.42 (![B: $i, C: $i] : (constant(C) | decreases(B) | increases(B) | (~constant(sum(B, C))))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[78, 77])).
% 0.12/0.42 tff(80,plain,
% 0.12/0.42 (![B: $i, C: $i] : (constant(C) | decreases(B) | increases(B) | (~constant(sum(B, C))))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[79, 71])).
% 0.12/0.42 tff(81,plain,(
% 0.12/0.42 ![B: $i, C: $i] : (constant(C) | decreases(B) | increases(B) | (~constant(sum(B, C))))),
% 0.12/0.42 inference(skolemize,[status(sab)],[80])).
% 0.12/0.42 tff(82,plain,
% 0.12/0.42 (![B: $i, C: $i] : (constant(C) | decreases(B) | increases(B) | (~constant(sum(B, C))))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[81, 70])).
% 0.12/0.42 tff(83,plain,
% 0.12/0.42 (((~![B: $i, C: $i] : (constant(C) | decreases(B) | increases(B) | (~constant(sum(B, C))))) | (constant(cardinality_at_time(efficient_producers, sk2)) | decreases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))) <=> ((~![B: $i, C: $i] : (constant(C) | decreases(B) | increases(B) | (~constant(sum(B, C))))) | constant(cardinality_at_time(efficient_producers, sk2)) | decreases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))),
% 0.12/0.42 inference(rewrite,[status(thm)],[])).
% 0.12/0.42 tff(84,plain,
% 0.12/0.42 ((~![B: $i, C: $i] : (constant(C) | decreases(B) | increases(B) | (~constant(sum(B, C))))) | (constant(cardinality_at_time(efficient_producers, sk2)) | decreases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))),
% 0.12/0.42 inference(quant_inst,[status(thm)],[])).
% 0.12/0.42 tff(85,plain,
% 0.12/0.42 ((~![B: $i, C: $i] : (constant(C) | decreases(B) | increases(B) | (~constant(sum(B, C))))) | constant(cardinality_at_time(efficient_producers, sk2)) | decreases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[84, 83])).
% 0.12/0.42 tff(86,plain,
% 0.12/0.42 (constant(cardinality_at_time(efficient_producers, sk2)) | decreases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))))),
% 0.12/0.42 inference(unit_resolution,[status(thm)],[85, 82])).
% 0.12/0.42 tff(87,plain,
% 0.12/0.42 (constant(cardinality_at_time(efficient_producers, sk2)) | decreases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(first_movers, sk2))),
% 0.12/0.42 inference(unit_resolution,[status(thm)],[86, 68])).
% 0.12/0.42 tff(88,plain,
% 0.12/0.42 (constant(cardinality_at_time(efficient_producers, sk2))),
% 0.12/0.42 inference(unit_resolution,[status(thm)],[87, 2, 1])).
% 0.12/0.42 tff(89,plain,
% 0.12/0.42 (^[B: $i, A: $i] : refl(((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | greater(cardinality_at_time(efficient_producers, B), zero)) <=> ((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | greater(cardinality_at_time(efficient_producers, B), zero)))),
% 0.12/0.42 inference(bind,[status(th)],[])).
% 0.12/0.42 tff(90,plain,
% 0.12/0.42 (![B: $i, A: $i] : ((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | greater(cardinality_at_time(efficient_producers, B), zero)) <=> ![B: $i, A: $i] : ((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | greater(cardinality_at_time(efficient_producers, B), zero))),
% 0.12/0.42 inference(quant_intro,[status(thm)],[89])).
% 0.12/0.42 tff(91,plain,
% 0.12/0.42 (![B: $i, A: $i] : ((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | greater(cardinality_at_time(efficient_producers, B), zero)) <=> ![B: $i, A: $i] : ((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | greater(cardinality_at_time(efficient_producers, B), zero))),
% 0.12/0.42 inference(rewrite,[status(thm)],[])).
% 0.12/0.42 tff(92,plain,
% 0.12/0.42 (^[B: $i, A: $i] : rewrite((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | greater(cardinality_at_time(efficient_producers, B), zero)) <=> ((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | greater(cardinality_at_time(efficient_producers, B), zero)))),
% 0.12/0.42 inference(bind,[status(th)],[])).
% 0.12/0.42 tff(93,plain,
% 0.12/0.42 (![B: $i, A: $i] : (((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | greater(cardinality_at_time(efficient_producers, B), zero)) <=> ![B: $i, A: $i] : ((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | greater(cardinality_at_time(efficient_producers, B), zero))),
% 0.12/0.42 inference(quant_intro,[status(thm)],[92])).
% 0.12/0.42 tff(94,axiom,(![B: $i, A: $i] : (((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | greater(cardinality_at_time(efficient_producers, B), zero))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_non_zero_producers_44')).
% 0.12/0.42 tff(95,plain,
% 0.12/0.42 (![B: $i, A: $i] : ((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | greater(cardinality_at_time(efficient_producers, B), zero))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[94, 93])).
% 0.12/0.42 tff(96,plain,
% 0.12/0.42 (![B: $i, A: $i] : ((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | greater(cardinality_at_time(efficient_producers, B), zero))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[95, 91])).
% 0.12/0.42 tff(97,plain,(
% 0.12/0.42 ![B: $i, A: $i] : ((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | greater(cardinality_at_time(efficient_producers, B), zero))),
% 0.12/0.42 inference(skolemize,[status(sab)],[96])).
% 0.12/0.42 tff(98,plain,
% 0.12/0.42 (![B: $i, A: $i] : ((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | greater(cardinality_at_time(efficient_producers, B), zero))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[97, 90])).
% 0.12/0.42 tff(99,plain,
% 0.12/0.42 (((~![B: $i, A: $i] : ((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | greater(cardinality_at_time(efficient_producers, B), zero))) | ((~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | greater(cardinality_at_time(efficient_producers, sk2), zero))) <=> ((~![B: $i, A: $i] : ((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | greater(cardinality_at_time(efficient_producers, B), zero))) | (~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | greater(cardinality_at_time(efficient_producers, sk2), zero))),
% 0.12/0.42 inference(rewrite,[status(thm)],[])).
% 0.12/0.42 tff(100,plain,
% 0.12/0.42 ((~![B: $i, A: $i] : ((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | greater(cardinality_at_time(efficient_producers, B), zero))) | ((~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | greater(cardinality_at_time(efficient_producers, sk2), zero))),
% 0.12/0.42 inference(quant_inst,[status(thm)],[])).
% 0.12/0.42 tff(101,plain,
% 0.12/0.42 ((~![B: $i, A: $i] : ((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B)) | greater(cardinality_at_time(efficient_producers, B), zero))) | (~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | greater(cardinality_at_time(efficient_producers, sk2), zero)),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[100, 99])).
% 0.12/0.42 tff(102,plain,
% 0.12/0.42 (greater(cardinality_at_time(efficient_producers, sk2), zero)),
% 0.12/0.42 inference(unit_resolution,[status(thm)],[101, 98, 8, 5])).
% 0.12/0.42 tff(103,plain,
% 0.12/0.42 (^[B: $i, A: $i] : refl(((~in_environment(A, B)) | (~environment(A)) | subpopulation(efficient_producers, A, B)) <=> ((~in_environment(A, B)) | (~environment(A)) | subpopulation(efficient_producers, A, B)))),
% 0.12/0.42 inference(bind,[status(th)],[])).
% 0.12/0.42 tff(104,plain,
% 0.12/0.42 (![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(efficient_producers, A, B)) <=> ![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(efficient_producers, A, B))),
% 0.12/0.42 inference(quant_intro,[status(thm)],[103])).
% 0.12/0.42 tff(105,plain,
% 0.12/0.42 (![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(efficient_producers, A, B)) <=> ![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(efficient_producers, A, B))),
% 0.12/0.42 inference(rewrite,[status(thm)],[])).
% 0.12/0.42 tff(106,plain,
% 0.12/0.42 (^[B: $i, A: $i] : rewrite((((~environment(A)) | (~in_environment(A, B))) | subpopulation(efficient_producers, A, B)) <=> ((~in_environment(A, B)) | (~environment(A)) | subpopulation(efficient_producers, A, B)))),
% 0.12/0.42 inference(bind,[status(th)],[])).
% 0.12/0.42 tff(107,plain,
% 0.12/0.42 (![B: $i, A: $i] : (((~environment(A)) | (~in_environment(A, B))) | subpopulation(efficient_producers, A, B)) <=> ![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(efficient_producers, A, B))),
% 0.12/0.42 inference(quant_intro,[status(thm)],[106])).
% 0.12/0.42 tff(108,axiom,(![B: $i, A: $i] : (((~environment(A)) | (~in_environment(A, B))) | subpopulation(efficient_producers, A, B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_subpopulations_31')).
% 0.12/0.42 tff(109,plain,
% 0.12/0.42 (![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(efficient_producers, A, B))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[108, 107])).
% 0.12/0.42 tff(110,plain,
% 0.12/0.42 (![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(efficient_producers, A, B))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[109, 105])).
% 0.12/0.42 tff(111,plain,(
% 0.12/0.42 ![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(efficient_producers, A, B))),
% 0.12/0.42 inference(skolemize,[status(sab)],[110])).
% 0.12/0.42 tff(112,plain,
% 0.12/0.42 (![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(efficient_producers, A, B))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[111, 104])).
% 0.12/0.42 tff(113,plain,
% 0.12/0.42 (((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(efficient_producers, A, B))) | ((~environment(sk1)) | subpopulation(efficient_producers, sk1, sk2) | (~in_environment(sk1, sk2)))) <=> ((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(efficient_producers, A, B))) | (~environment(sk1)) | subpopulation(efficient_producers, sk1, sk2) | (~in_environment(sk1, sk2)))),
% 0.12/0.42 inference(rewrite,[status(thm)],[])).
% 0.12/0.42 tff(114,plain,
% 0.12/0.42 (((~in_environment(sk1, sk2)) | (~environment(sk1)) | subpopulation(efficient_producers, sk1, sk2)) <=> ((~environment(sk1)) | subpopulation(efficient_producers, sk1, sk2) | (~in_environment(sk1, sk2)))),
% 0.12/0.42 inference(rewrite,[status(thm)],[])).
% 0.12/0.42 tff(115,plain,
% 0.12/0.42 (((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(efficient_producers, A, B))) | ((~in_environment(sk1, sk2)) | (~environment(sk1)) | subpopulation(efficient_producers, sk1, sk2))) <=> ((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(efficient_producers, A, B))) | ((~environment(sk1)) | subpopulation(efficient_producers, sk1, sk2) | (~in_environment(sk1, sk2))))),
% 0.12/0.42 inference(monotonicity,[status(thm)],[114])).
% 0.12/0.42 tff(116,plain,
% 0.12/0.42 (((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(efficient_producers, A, B))) | ((~in_environment(sk1, sk2)) | (~environment(sk1)) | subpopulation(efficient_producers, sk1, sk2))) <=> ((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(efficient_producers, A, B))) | (~environment(sk1)) | subpopulation(efficient_producers, sk1, sk2) | (~in_environment(sk1, sk2)))),
% 0.12/0.42 inference(transitivity,[status(thm)],[115, 113])).
% 0.12/0.42 tff(117,plain,
% 0.12/0.42 ((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(efficient_producers, A, B))) | ((~in_environment(sk1, sk2)) | (~environment(sk1)) | subpopulation(efficient_producers, sk1, sk2))),
% 0.12/0.42 inference(quant_inst,[status(thm)],[])).
% 0.12/0.42 tff(118,plain,
% 0.12/0.42 ((~![B: $i, A: $i] : ((~in_environment(A, B)) | (~environment(A)) | subpopulation(efficient_producers, A, B))) | (~environment(sk1)) | subpopulation(efficient_producers, sk1, sk2) | (~in_environment(sk1, sk2))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[117, 116])).
% 0.12/0.42 tff(119,plain,
% 0.12/0.42 (subpopulation(efficient_producers, sk1, sk2)),
% 0.12/0.42 inference(unit_resolution,[status(thm)],[118, 112, 8, 22])).
% 0.12/0.42 tff(120,plain,
% 0.12/0.42 (^[B: $i, A: $i, C: $i] : refl(((~environment(A)) | (growth_rate(C, B) = zero) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B))) <=> ((~environment(A)) | (growth_rate(C, B) = zero) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B))))),
% 0.12/0.42 inference(bind,[status(th)],[])).
% 0.12/0.42 tff(121,plain,
% 0.12/0.42 (![B: $i, A: $i, C: $i] : ((~environment(A)) | (growth_rate(C, B) = zero) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B))) <=> ![B: $i, A: $i, C: $i] : ((~environment(A)) | (growth_rate(C, B) = zero) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))),
% 0.12/0.42 inference(quant_intro,[status(thm)],[120])).
% 0.12/0.42 tff(122,plain,
% 0.12/0.42 (![B: $i, A: $i, C: $i] : ((~environment(A)) | (growth_rate(C, B) = zero) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B))) <=> ![B: $i, A: $i, C: $i] : ((~environment(A)) | (growth_rate(C, B) = zero) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))),
% 0.12/0.42 inference(rewrite,[status(thm)],[])).
% 0.12/0.42 tff(123,plain,
% 0.12/0.42 (^[B: $i, A: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~environment(A)) | (~in_environment(A, B))) | (~subpopulation(C, A, B))) <=> ((~environment(A)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))), (((((~environment(A)) | (~in_environment(A, B))) | (~subpopulation(C, A, B))) | (~greater(cardinality_at_time(C, B), zero))) <=> (((~environment(A)) | (~subpopulation(C, A, B)) | (~in_environment(A, B))) | (~greater(cardinality_at_time(C, B), zero))))), rewrite((((~environment(A)) | (~subpopulation(C, A, B)) | (~in_environment(A, B))) | (~greater(cardinality_at_time(C, B), zero))) <=> ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))), (((((~environment(A)) | (~in_environment(A, B))) | (~subpopulation(C, A, B))) | (~greater(cardinality_at_time(C, B), zero))) <=> ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B))))), ((((((~environment(A)) | (~in_environment(A, B))) | (~subpopulation(C, A, B))) | (~greater(cardinality_at_time(C, B), zero))) | (~constant(cardinality_at_time(C, B)))) <=> (((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B))) | (~constant(cardinality_at_time(C, B)))))), rewrite((((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B))) | (~constant(cardinality_at_time(C, B)))) <=> ((~environment(A)) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))), ((((((~environment(A)) | (~in_environment(A, B))) | (~subpopulation(C, A, B))) | (~greater(cardinality_at_time(C, B), zero))) | (~constant(cardinality_at_time(C, B)))) <=> ((~environment(A)) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B))))), (((((((~environment(A)) | (~in_environment(A, B))) | (~subpopulation(C, A, B))) | (~greater(cardinality_at_time(C, B), zero))) | (~constant(cardinality_at_time(C, B)))) | (growth_rate(C, B) = zero)) <=> (((~environment(A)) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B))) | (growth_rate(C, B) = zero)))), rewrite((((~environment(A)) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B))) | (growth_rate(C, B) = zero)) <=> ((~environment(A)) | (growth_rate(C, B) = zero) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))), (((((((~environment(A)) | (~in_environment(A, B))) | (~subpopulation(C, A, B))) | (~greater(cardinality_at_time(C, B), zero))) | (~constant(cardinality_at_time(C, B)))) | (growth_rate(C, B) = zero)) <=> ((~environment(A)) | (growth_rate(C, B) = zero) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))))),
% 0.12/0.42 inference(bind,[status(th)],[])).
% 0.12/0.42 tff(124,plain,
% 0.12/0.42 (![B: $i, A: $i, C: $i] : ((((((~environment(A)) | (~in_environment(A, B))) | (~subpopulation(C, A, B))) | (~greater(cardinality_at_time(C, B), zero))) | (~constant(cardinality_at_time(C, B)))) | (growth_rate(C, B) = zero)) <=> ![B: $i, A: $i, C: $i] : ((~environment(A)) | (growth_rate(C, B) = zero) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))),
% 0.12/0.42 inference(quant_intro,[status(thm)],[123])).
% 0.12/0.42 tff(125,axiom,(![B: $i, A: $i, C: $i] : ((((((~environment(A)) | (~in_environment(A, B))) | (~subpopulation(C, A, B))) | (~greater(cardinality_at_time(C, B), zero))) | (~constant(cardinality_at_time(C, B)))) | (growth_rate(C, B) = zero))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_growth_rate_40')).
% 0.12/0.42 tff(126,plain,
% 0.12/0.42 (![B: $i, A: $i, C: $i] : ((~environment(A)) | (growth_rate(C, B) = zero) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[125, 124])).
% 0.12/0.42 tff(127,plain,
% 0.12/0.42 (![B: $i, A: $i, C: $i] : ((~environment(A)) | (growth_rate(C, B) = zero) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))),
% 0.12/0.42 inference(modus_ponens,[status(thm)],[126, 122])).
% 0.12/0.42 tff(128,plain,(
% 0.12/0.42 ![B: $i, A: $i, C: $i] : ((~environment(A)) | (growth_rate(C, B) = zero) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))),
% 0.12/0.42 inference(skolemize,[status(sab)],[127])).
% 0.12/0.42 tff(129,plain,
% 0.12/0.42 (![B: $i, A: $i, C: $i] : ((~environment(A)) | (growth_rate(C, B) = zero) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))),
% 0.12/0.43 inference(modus_ponens,[status(thm)],[128, 121])).
% 0.12/0.43 tff(130,plain,
% 0.12/0.43 (((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (growth_rate(C, B) = zero) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))) | ((growth_rate(efficient_producers, sk2) = zero) | (~environment(sk1)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~constant(cardinality_at_time(efficient_producers, sk2))))) <=> ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (growth_rate(C, B) = zero) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))) | (growth_rate(efficient_producers, sk2) = zero) | (~environment(sk1)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~constant(cardinality_at_time(efficient_producers, sk2))))),
% 0.12/0.43 inference(rewrite,[status(thm)],[])).
% 0.12/0.43 tff(131,plain,
% 0.12/0.43 (((~environment(sk1)) | (growth_rate(efficient_producers, sk2) = zero) | (~constant(cardinality_at_time(efficient_producers, sk2))) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~in_environment(sk1, sk2))) <=> ((growth_rate(efficient_producers, sk2) = zero) | (~environment(sk1)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~constant(cardinality_at_time(efficient_producers, sk2))))),
% 0.12/0.43 inference(rewrite,[status(thm)],[])).
% 0.12/0.43 tff(132,plain,
% 0.12/0.43 (((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (growth_rate(C, B) = zero) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))) | ((~environment(sk1)) | (growth_rate(efficient_producers, sk2) = zero) | (~constant(cardinality_at_time(efficient_producers, sk2))) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~in_environment(sk1, sk2)))) <=> ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (growth_rate(C, B) = zero) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))) | ((growth_rate(efficient_producers, sk2) = zero) | (~environment(sk1)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~constant(cardinality_at_time(efficient_producers, sk2)))))),
% 0.12/0.43 inference(monotonicity,[status(thm)],[131])).
% 0.12/0.43 tff(133,plain,
% 0.12/0.43 (((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (growth_rate(C, B) = zero) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))) | ((~environment(sk1)) | (growth_rate(efficient_producers, sk2) = zero) | (~constant(cardinality_at_time(efficient_producers, sk2))) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~in_environment(sk1, sk2)))) <=> ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (growth_rate(C, B) = zero) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))) | (growth_rate(efficient_producers, sk2) = zero) | (~environment(sk1)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~constant(cardinality_at_time(efficient_producers, sk2))))),
% 0.12/0.43 inference(transitivity,[status(thm)],[132, 130])).
% 0.12/0.43 tff(134,plain,
% 0.12/0.43 ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (growth_rate(C, B) = zero) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))) | ((~environment(sk1)) | (growth_rate(efficient_producers, sk2) = zero) | (~constant(cardinality_at_time(efficient_producers, sk2))) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~in_environment(sk1, sk2)))),
% 0.12/0.43 inference(quant_inst,[status(thm)],[])).
% 0.12/0.43 tff(135,plain,
% 0.12/0.43 ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (growth_rate(C, B) = zero) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))) | (growth_rate(efficient_producers, sk2) = zero) | (~environment(sk1)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~constant(cardinality_at_time(efficient_producers, sk2)))),
% 0.12/0.43 inference(modus_ponens,[status(thm)],[134, 133])).
% 0.12/0.43 tff(136,plain,
% 0.12/0.43 ((growth_rate(efficient_producers, sk2) = zero) | (~constant(cardinality_at_time(efficient_producers, sk2)))),
% 0.12/0.43 inference(unit_resolution,[status(thm)],[135, 129, 8, 119, 22, 102])).
% 0.12/0.43 tff(137,plain,
% 0.12/0.43 (growth_rate(efficient_producers, sk2) = zero),
% 0.12/0.43 inference(unit_resolution,[status(thm)],[136, 88])).
% 0.12/0.43 tff(138,plain,
% 0.12/0.43 (^[B: $i, C: $i] : refl((constant(B) | decreases(B) | increases(B) | (~constant(sum(B, C)))) <=> (constant(B) | decreases(B) | increases(B) | (~constant(sum(B, C)))))),
% 0.12/0.43 inference(bind,[status(th)],[])).
% 0.12/0.43 tff(139,plain,
% 0.12/0.43 (![B: $i, C: $i] : (constant(B) | decreases(B) | increases(B) | (~constant(sum(B, C)))) <=> ![B: $i, C: $i] : (constant(B) | decreases(B) | increases(B) | (~constant(sum(B, C))))),
% 0.12/0.43 inference(quant_intro,[status(thm)],[138])).
% 0.12/0.43 tff(140,plain,
% 0.12/0.43 (![B: $i, C: $i] : (constant(B) | decreases(B) | increases(B) | (~constant(sum(B, C)))) <=> ![B: $i, C: $i] : (constant(B) | decreases(B) | increases(B) | (~constant(sum(B, C))))),
% 0.12/0.43 inference(rewrite,[status(thm)],[])).
% 0.12/0.43 tff(141,plain,
% 0.12/0.43 (^[B: $i, C: $i] : rewrite((decreases(B) | increases(B) | constant(B) | (~constant(sum(B, C)))) <=> (constant(B) | decreases(B) | increases(B) | (~constant(sum(B, C)))))),
% 0.12/0.43 inference(bind,[status(th)],[])).
% 0.12/0.43 tff(142,plain,
% 0.12/0.43 (![B: $i, C: $i] : (decreases(B) | increases(B) | constant(B) | (~constant(sum(B, C)))) <=> ![B: $i, C: $i] : (constant(B) | decreases(B) | increases(B) | (~constant(sum(B, C))))),
% 0.12/0.43 inference(quant_intro,[status(thm)],[141])).
% 0.12/0.43 tff(143,plain,
% 0.12/0.43 (![B: $i, A: $i, C: $i] : (decreases(B) | increases(B) | constant(B) | (~constant(sum(B, C)))) <=> ![B: $i, C: $i] : (decreases(B) | increases(B) | constant(B) | (~constant(sum(B, C))))),
% 0.12/0.43 inference(elim_unused_vars,[status(thm)],[])).
% 0.12/0.43 tff(144,plain,
% 0.12/0.43 (![B: $i, A: $i, C: $i] : (decreases(B) | increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C)))) <=> ![B: $i, A: $i, C: $i] : (decreases(B) | increases(B) | constant(B) | (~constant(sum(B, C))))),
% 0.12/0.43 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.12/0.43 tff(145,plain,
% 0.12/0.43 (![B: $i, A: $i, C: $i] : (decreases(B) | increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C)))) <=> ![B: $i, C: $i] : (decreases(B) | increases(B) | constant(B) | (~constant(sum(B, C))))),
% 0.12/0.43 inference(transitivity,[status(thm)],[144, 143])).
% 0.12/0.43 tff(146,plain,
% 0.12/0.43 (![B: $i, A: $i, C: $i] : (decreases(B) | increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C)))) <=> ![B: $i, C: $i] : (constant(B) | decreases(B) | increases(B) | (~constant(sum(B, C))))),
% 0.12/0.43 inference(transitivity,[status(thm)],[145, 142])).
% 0.12/0.43 tff(147,plain,
% 0.12/0.43 (^[B: $i, A: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~(A = sum(B, C))) | (~constant(A))) <=> ((~constant(A)) | (~(A = sum(B, C))))), ((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) <=> (((~constant(A)) | (~(A = sum(B, C)))) | constant(B)))), rewrite((((~constant(A)) | (~(A = sum(B, C)))) | constant(B)) <=> (constant(B) | (~constant(A)) | (~(A = sum(B, C))))), ((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) <=> (constant(B) | (~constant(A)) | (~(A = sum(B, C)))))), (((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) | increases(B)) <=> ((constant(B) | (~constant(A)) | (~(A = sum(B, C)))) | increases(B)))), rewrite(((constant(B) | (~constant(A)) | (~(A = sum(B, C)))) | increases(B)) <=> (increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))))), (((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) | increases(B)) <=> (increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C)))))), ((((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) | increases(B)) | decreases(B)) <=> ((increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C)))) | decreases(B)))), rewrite(((increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C)))) | decreases(B)) <=> (decreases(B) | increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))))), ((((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) | increases(B)) | decreases(B)) <=> (decreases(B) | increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))))))),
% 0.12/0.43 inference(bind,[status(th)],[])).
% 0.12/0.43 tff(148,plain,
% 0.12/0.43 (![B: $i, A: $i, C: $i] : (((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) | increases(B)) | decreases(B)) <=> ![B: $i, A: $i, C: $i] : (decreases(B) | increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))))),
% 0.12/0.43 inference(quant_intro,[status(thm)],[147])).
% 0.12/0.43 tff(149,plain,
% 0.12/0.43 (![B: $i, A: $i, C: $i] : (((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) | increases(B)) | decreases(B)) <=> ![B: $i, C: $i] : (constant(B) | decreases(B) | increases(B) | (~constant(sum(B, C))))),
% 0.12/0.43 inference(transitivity,[status(thm)],[148, 146])).
% 0.12/0.43 tff(150,axiom,(![B: $i, A: $i, C: $i] : (((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) | increases(B)) | decreases(B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_abc_sum_increase_32')).
% 0.12/0.43 tff(151,plain,
% 0.12/0.43 (![B: $i, C: $i] : (constant(B) | decreases(B) | increases(B) | (~constant(sum(B, C))))),
% 0.12/0.43 inference(modus_ponens,[status(thm)],[150, 149])).
% 0.12/0.43 tff(152,plain,
% 0.12/0.43 (![B: $i, C: $i] : (constant(B) | decreases(B) | increases(B) | (~constant(sum(B, C))))),
% 0.12/0.43 inference(modus_ponens,[status(thm)],[151, 140])).
% 0.12/0.43 tff(153,plain,(
% 0.12/0.43 ![B: $i, C: $i] : (constant(B) | decreases(B) | increases(B) | (~constant(sum(B, C))))),
% 0.12/0.43 inference(skolemize,[status(sab)],[152])).
% 0.12/0.43 tff(154,plain,
% 0.12/0.43 (![B: $i, C: $i] : (constant(B) | decreases(B) | increases(B) | (~constant(sum(B, C))))),
% 0.12/0.43 inference(modus_ponens,[status(thm)],[153, 139])).
% 0.12/0.43 tff(155,plain,
% 0.12/0.43 (((~![B: $i, C: $i] : (constant(B) | decreases(B) | increases(B) | (~constant(sum(B, C))))) | (constant(cardinality_at_time(first_movers, sk2)) | decreases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))) <=> ((~![B: $i, C: $i] : (constant(B) | decreases(B) | increases(B) | (~constant(sum(B, C))))) | constant(cardinality_at_time(first_movers, sk2)) | decreases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))),
% 0.12/0.43 inference(rewrite,[status(thm)],[])).
% 0.12/0.43 tff(156,plain,
% 0.12/0.43 ((~![B: $i, C: $i] : (constant(B) | decreases(B) | increases(B) | (~constant(sum(B, C))))) | (constant(cardinality_at_time(first_movers, sk2)) | decreases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))),
% 0.12/0.43 inference(quant_inst,[status(thm)],[])).
% 0.12/0.43 tff(157,plain,
% 0.12/0.43 ((~![B: $i, C: $i] : (constant(B) | decreases(B) | increases(B) | (~constant(sum(B, C))))) | constant(cardinality_at_time(first_movers, sk2)) | decreases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))))),
% 0.12/0.43 inference(modus_ponens,[status(thm)],[156, 155])).
% 0.12/0.43 tff(158,plain,
% 0.12/0.43 (constant(cardinality_at_time(first_movers, sk2)) | decreases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))))),
% 0.12/0.43 inference(unit_resolution,[status(thm)],[157, 154])).
% 0.12/0.43 tff(159,plain,
% 0.12/0.43 (constant(cardinality_at_time(first_movers, sk2)) | decreases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(first_movers, sk2))),
% 0.12/0.43 inference(unit_resolution,[status(thm)],[158, 68])).
% 0.12/0.43 tff(160,plain,
% 0.12/0.43 (constant(cardinality_at_time(first_movers, sk2))),
% 0.12/0.43 inference(unit_resolution,[status(thm)],[159, 2, 1])).
% 0.12/0.43 tff(161,plain,
% 0.12/0.43 (^[B: $i, A: $i] : refl(((~environment(A)) | greater(cardinality_at_time(first_movers, B), zero) | (~subpopulations(first_movers, efficient_producers, A, B))) <=> ((~environment(A)) | greater(cardinality_at_time(first_movers, B), zero) | (~subpopulations(first_movers, efficient_producers, A, B))))),
% 0.12/0.43 inference(bind,[status(th)],[])).
% 0.12/0.43 tff(162,plain,
% 0.12/0.43 (![B: $i, A: $i] : ((~environment(A)) | greater(cardinality_at_time(first_movers, B), zero) | (~subpopulations(first_movers, efficient_producers, A, B))) <=> ![B: $i, A: $i] : ((~environment(A)) | greater(cardinality_at_time(first_movers, B), zero) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.12/0.43 inference(quant_intro,[status(thm)],[161])).
% 0.12/0.43 tff(163,plain,
% 0.12/0.43 (![B: $i, A: $i] : ((~environment(A)) | greater(cardinality_at_time(first_movers, B), zero) | (~subpopulations(first_movers, efficient_producers, A, B))) <=> ![B: $i, A: $i] : ((~environment(A)) | greater(cardinality_at_time(first_movers, B), zero) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.12/0.43 inference(rewrite,[status(thm)],[])).
% 0.12/0.43 tff(164,plain,
% 0.12/0.43 (^[B: $i, A: $i] : rewrite((((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | greater(cardinality_at_time(first_movers, B), zero)) <=> ((~environment(A)) | greater(cardinality_at_time(first_movers, B), zero) | (~subpopulations(first_movers, efficient_producers, A, B))))),
% 0.12/0.43 inference(bind,[status(th)],[])).
% 0.12/0.43 tff(165,plain,
% 0.12/0.43 (![B: $i, A: $i] : (((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | greater(cardinality_at_time(first_movers, B), zero)) <=> ![B: $i, A: $i] : ((~environment(A)) | greater(cardinality_at_time(first_movers, B), zero) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.12/0.43 inference(quant_intro,[status(thm)],[164])).
% 0.12/0.43 tff(166,axiom,(![B: $i, A: $i] : (((~environment(A)) | (~subpopulations(first_movers, efficient_producers, A, B))) | greater(cardinality_at_time(first_movers, B), zero))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_non_zero_producers_43')).
% 0.12/0.43 tff(167,plain,
% 0.12/0.43 (![B: $i, A: $i] : ((~environment(A)) | greater(cardinality_at_time(first_movers, B), zero) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.12/0.43 inference(modus_ponens,[status(thm)],[166, 165])).
% 0.12/0.43 tff(168,plain,
% 0.12/0.43 (![B: $i, A: $i] : ((~environment(A)) | greater(cardinality_at_time(first_movers, B), zero) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.12/0.43 inference(modus_ponens,[status(thm)],[167, 163])).
% 0.12/0.43 tff(169,plain,(
% 0.12/0.43 ![B: $i, A: $i] : ((~environment(A)) | greater(cardinality_at_time(first_movers, B), zero) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.12/0.43 inference(skolemize,[status(sab)],[168])).
% 0.12/0.43 tff(170,plain,
% 0.12/0.43 (![B: $i, A: $i] : ((~environment(A)) | greater(cardinality_at_time(first_movers, B), zero) | (~subpopulations(first_movers, efficient_producers, A, B)))),
% 0.12/0.43 inference(modus_ponens,[status(thm)],[169, 162])).
% 0.12/0.43 tff(171,plain,
% 0.12/0.43 (((~![B: $i, A: $i] : ((~environment(A)) | greater(cardinality_at_time(first_movers, B), zero) | (~subpopulations(first_movers, efficient_producers, A, B)))) | ((~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | greater(cardinality_at_time(first_movers, sk2), zero))) <=> ((~![B: $i, A: $i] : ((~environment(A)) | greater(cardinality_at_time(first_movers, B), zero) | (~subpopulations(first_movers, efficient_producers, A, B)))) | (~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | greater(cardinality_at_time(first_movers, sk2), zero))),
% 0.12/0.43 inference(rewrite,[status(thm)],[])).
% 0.12/0.43 tff(172,plain,
% 0.12/0.43 (((~environment(sk1)) | greater(cardinality_at_time(first_movers, sk2), zero) | (~subpopulations(first_movers, efficient_producers, sk1, sk2))) <=> ((~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | greater(cardinality_at_time(first_movers, sk2), zero))),
% 0.12/0.43 inference(rewrite,[status(thm)],[])).
% 0.12/0.43 tff(173,plain,
% 0.12/0.43 (((~![B: $i, A: $i] : ((~environment(A)) | greater(cardinality_at_time(first_movers, B), zero) | (~subpopulations(first_movers, efficient_producers, A, B)))) | ((~environment(sk1)) | greater(cardinality_at_time(first_movers, sk2), zero) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)))) <=> ((~![B: $i, A: $i] : ((~environment(A)) | greater(cardinality_at_time(first_movers, B), zero) | (~subpopulations(first_movers, efficient_producers, A, B)))) | ((~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | greater(cardinality_at_time(first_movers, sk2), zero)))),
% 0.12/0.43 inference(monotonicity,[status(thm)],[172])).
% 0.12/0.43 tff(174,plain,
% 0.12/0.43 (((~![B: $i, A: $i] : ((~environment(A)) | greater(cardinality_at_time(first_movers, B), zero) | (~subpopulations(first_movers, efficient_producers, A, B)))) | ((~environment(sk1)) | greater(cardinality_at_time(first_movers, sk2), zero) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)))) <=> ((~![B: $i, A: $i] : ((~environment(A)) | greater(cardinality_at_time(first_movers, B), zero) | (~subpopulations(first_movers, efficient_producers, A, B)))) | (~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | greater(cardinality_at_time(first_movers, sk2), zero))),
% 0.12/0.43 inference(transitivity,[status(thm)],[173, 171])).
% 0.12/0.43 tff(175,plain,
% 0.12/0.43 ((~![B: $i, A: $i] : ((~environment(A)) | greater(cardinality_at_time(first_movers, B), zero) | (~subpopulations(first_movers, efficient_producers, A, B)))) | ((~environment(sk1)) | greater(cardinality_at_time(first_movers, sk2), zero) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)))),
% 0.12/0.43 inference(quant_inst,[status(thm)],[])).
% 0.12/0.43 tff(176,plain,
% 0.12/0.43 ((~![B: $i, A: $i] : ((~environment(A)) | greater(cardinality_at_time(first_movers, B), zero) | (~subpopulations(first_movers, efficient_producers, A, B)))) | (~environment(sk1)) | (~subpopulations(first_movers, efficient_producers, sk1, sk2)) | greater(cardinality_at_time(first_movers, sk2), zero)),
% 0.12/0.43 inference(modus_ponens,[status(thm)],[175, 174])).
% 0.12/0.43 tff(177,plain,
% 0.12/0.43 (greater(cardinality_at_time(first_movers, sk2), zero)),
% 0.12/0.43 inference(unit_resolution,[status(thm)],[176, 170, 8, 5])).
% 0.12/0.43 tff(178,plain,
% 0.12/0.43 (((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (growth_rate(C, B) = zero) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))) | ((growth_rate(first_movers, sk2) = zero) | (~environment(sk1)) | (~subpopulation(first_movers, sk1, sk2)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~constant(cardinality_at_time(first_movers, sk2))))) <=> ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (growth_rate(C, B) = zero) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))) | (growth_rate(first_movers, sk2) = zero) | (~environment(sk1)) | (~subpopulation(first_movers, sk1, sk2)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~constant(cardinality_at_time(first_movers, sk2))))),
% 0.12/0.43 inference(rewrite,[status(thm)],[])).
% 0.12/0.43 tff(179,plain,
% 0.12/0.43 (((~environment(sk1)) | (growth_rate(first_movers, sk2) = zero) | (~constant(cardinality_at_time(first_movers, sk2))) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~subpopulation(first_movers, sk1, sk2)) | (~in_environment(sk1, sk2))) <=> ((growth_rate(first_movers, sk2) = zero) | (~environment(sk1)) | (~subpopulation(first_movers, sk1, sk2)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~constant(cardinality_at_time(first_movers, sk2))))),
% 0.12/0.44 inference(rewrite,[status(thm)],[])).
% 0.12/0.44 tff(180,plain,
% 0.12/0.44 (((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (growth_rate(C, B) = zero) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))) | ((~environment(sk1)) | (growth_rate(first_movers, sk2) = zero) | (~constant(cardinality_at_time(first_movers, sk2))) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~subpopulation(first_movers, sk1, sk2)) | (~in_environment(sk1, sk2)))) <=> ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (growth_rate(C, B) = zero) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))) | ((growth_rate(first_movers, sk2) = zero) | (~environment(sk1)) | (~subpopulation(first_movers, sk1, sk2)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~constant(cardinality_at_time(first_movers, sk2)))))),
% 0.12/0.44 inference(monotonicity,[status(thm)],[179])).
% 0.12/0.44 tff(181,plain,
% 0.12/0.44 (((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (growth_rate(C, B) = zero) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))) | ((~environment(sk1)) | (growth_rate(first_movers, sk2) = zero) | (~constant(cardinality_at_time(first_movers, sk2))) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~subpopulation(first_movers, sk1, sk2)) | (~in_environment(sk1, sk2)))) <=> ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (growth_rate(C, B) = zero) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))) | (growth_rate(first_movers, sk2) = zero) | (~environment(sk1)) | (~subpopulation(first_movers, sk1, sk2)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~constant(cardinality_at_time(first_movers, sk2))))),
% 0.12/0.44 inference(transitivity,[status(thm)],[180, 178])).
% 0.12/0.44 tff(182,plain,
% 0.12/0.44 ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (growth_rate(C, B) = zero) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))) | ((~environment(sk1)) | (growth_rate(first_movers, sk2) = zero) | (~constant(cardinality_at_time(first_movers, sk2))) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~subpopulation(first_movers, sk1, sk2)) | (~in_environment(sk1, sk2)))),
% 0.12/0.44 inference(quant_inst,[status(thm)],[])).
% 0.12/0.44 tff(183,plain,
% 0.12/0.44 ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (growth_rate(C, B) = zero) | (~constant(cardinality_at_time(C, B))) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))) | (growth_rate(first_movers, sk2) = zero) | (~environment(sk1)) | (~subpopulation(first_movers, sk1, sk2)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~constant(cardinality_at_time(first_movers, sk2)))),
% 0.12/0.44 inference(modus_ponens,[status(thm)],[182, 181])).
% 0.12/0.44 tff(184,plain,
% 0.12/0.44 ((growth_rate(first_movers, sk2) = zero) | (~constant(cardinality_at_time(first_movers, sk2)))),
% 0.12/0.44 inference(unit_resolution,[status(thm)],[183, 129, 8, 39, 22, 177])).
% 0.12/0.44 tff(185,plain,
% 0.12/0.44 (growth_rate(first_movers, sk2) = zero),
% 0.12/0.44 inference(unit_resolution,[status(thm)],[184, 160])).
% 0.12/0.44 tff(186,plain,
% 0.12/0.44 (((~(growth_rate(first_movers, sk2) = zero)) | (~(growth_rate(efficient_producers, sk2) = zero))) <=> ((~(growth_rate(first_movers, sk2) = zero)) | (~(growth_rate(efficient_producers, sk2) = zero)))),
% 0.12/0.44 inference(rewrite,[status(thm)],[])).
% 0.12/0.44 tff(187,axiom,((~(growth_rate(first_movers, sk2) = zero)) | (~(growth_rate(efficient_producers, sk2) = zero))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_l7_50')).
% 0.12/0.44 tff(188,plain,
% 0.12/0.44 ((~(growth_rate(first_movers, sk2) = zero)) | (~(growth_rate(efficient_producers, sk2) = zero))),
% 0.12/0.44 inference(modus_ponens,[status(thm)],[187, 186])).
% 0.12/0.44 tff(189,plain,
% 0.12/0.44 ((~(growth_rate(first_movers, sk2) = zero)) | (~(growth_rate(efficient_producers, sk2) = zero))),
% 0.12/0.44 inference(modus_ponens,[status(thm)],[188, 186])).
% 0.12/0.44 tff(190,plain,
% 0.12/0.44 ((~(growth_rate(first_movers, sk2) = zero)) | (~(growth_rate(efficient_producers, sk2) = zero))),
% 0.12/0.44 inference(modus_ponens,[status(thm)],[189, 186])).
% 0.12/0.44 tff(191,plain,
% 0.12/0.44 ((~(growth_rate(first_movers, sk2) = zero)) | (~(growth_rate(efficient_producers, sk2) = zero))),
% 0.12/0.44 inference(modus_ponens,[status(thm)],[190, 186])).
% 0.12/0.44 tff(192,plain,
% 0.12/0.44 ((~(growth_rate(first_movers, sk2) = zero)) | (~(growth_rate(efficient_producers, sk2) = zero))),
% 0.12/0.44 inference(modus_ponens,[status(thm)],[191, 186])).
% 0.12/0.44 tff(193,plain,
% 0.12/0.44 ($false),
% 0.12/0.44 inference(unit_resolution,[status(thm)],[192, 185, 137])).
% 0.12/0.44 tff(194,plain,(decreases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(first_movers, sk2))), inference(lemma,lemma(discharge,[]))).
% 0.12/0.44 tff(195,plain,
% 0.12/0.44 (decreases(cardinality_at_time(first_movers, sk2))),
% 0.12/0.44 inference(unit_resolution,[status(thm)],[194, 1])).
% 0.12/0.44 tff(196,plain,
% 0.12/0.44 (^[B: $i, A: $i, C: $i] : refl(((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(zero, growth_rate(C, B)) | (~decreases(cardinality_at_time(C, B)))) <=> ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(zero, growth_rate(C, B)) | (~decreases(cardinality_at_time(C, B)))))),
% 0.12/0.44 inference(bind,[status(th)],[])).
% 0.12/0.44 tff(197,plain,
% 0.12/0.44 (![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(zero, growth_rate(C, B)) | (~decreases(cardinality_at_time(C, B)))) <=> ![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(zero, growth_rate(C, B)) | (~decreases(cardinality_at_time(C, B))))),
% 0.12/0.44 inference(quant_intro,[status(thm)],[196])).
% 0.12/0.44 tff(198,plain,
% 0.12/0.44 (![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(zero, growth_rate(C, B)) | (~decreases(cardinality_at_time(C, B)))) <=> ![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(zero, growth_rate(C, B)) | (~decreases(cardinality_at_time(C, B))))),
% 0.12/0.44 inference(rewrite,[status(thm)],[])).
% 0.12/0.44 tff(199,plain,
% 0.12/0.44 (^[B: $i, A: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~environment(A)) | (~in_environment(A, B))) | (~subpopulation(C, A, B))) <=> ((~environment(A)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))), (((((~environment(A)) | (~in_environment(A, B))) | (~subpopulation(C, A, B))) | (~greater(cardinality_at_time(C, B), zero))) <=> (((~environment(A)) | (~subpopulation(C, A, B)) | (~in_environment(A, B))) | (~greater(cardinality_at_time(C, B), zero))))), rewrite((((~environment(A)) | (~subpopulation(C, A, B)) | (~in_environment(A, B))) | (~greater(cardinality_at_time(C, B), zero))) <=> ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))), (((((~environment(A)) | (~in_environment(A, B))) | (~subpopulation(C, A, B))) | (~greater(cardinality_at_time(C, B), zero))) <=> ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B))))), ((((((~environment(A)) | (~in_environment(A, B))) | (~subpopulation(C, A, B))) | (~greater(cardinality_at_time(C, B), zero))) | (~decreases(cardinality_at_time(C, B)))) <=> (((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B))) | (~decreases(cardinality_at_time(C, B)))))), rewrite((((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B))) | (~decreases(cardinality_at_time(C, B)))) <=> ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | (~decreases(cardinality_at_time(C, B))))), ((((((~environment(A)) | (~in_environment(A, B))) | (~subpopulation(C, A, B))) | (~greater(cardinality_at_time(C, B), zero))) | (~decreases(cardinality_at_time(C, B)))) <=> ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | (~decreases(cardinality_at_time(C, B)))))), (((((((~environment(A)) | (~in_environment(A, B))) | (~subpopulation(C, A, B))) | (~greater(cardinality_at_time(C, B), zero))) | (~decreases(cardinality_at_time(C, B)))) | greater(zero, growth_rate(C, B))) <=> (((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | (~decreases(cardinality_at_time(C, B)))) | greater(zero, growth_rate(C, B))))), rewrite((((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | (~decreases(cardinality_at_time(C, B)))) | greater(zero, growth_rate(C, B))) <=> ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(zero, growth_rate(C, B)) | (~decreases(cardinality_at_time(C, B))))), (((((((~environment(A)) | (~in_environment(A, B))) | (~subpopulation(C, A, B))) | (~greater(cardinality_at_time(C, B), zero))) | (~decreases(cardinality_at_time(C, B)))) | greater(zero, growth_rate(C, B))) <=> ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(zero, growth_rate(C, B)) | (~decreases(cardinality_at_time(C, B))))))),
% 0.12/0.44 inference(bind,[status(th)],[])).
% 0.12/0.44 tff(200,plain,
% 0.12/0.44 (![B: $i, A: $i, C: $i] : ((((((~environment(A)) | (~in_environment(A, B))) | (~subpopulation(C, A, B))) | (~greater(cardinality_at_time(C, B), zero))) | (~decreases(cardinality_at_time(C, B)))) | greater(zero, growth_rate(C, B))) <=> ![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(zero, growth_rate(C, B)) | (~decreases(cardinality_at_time(C, B))))),
% 0.12/0.44 inference(quant_intro,[status(thm)],[199])).
% 0.12/0.44 tff(201,axiom,(![B: $i, A: $i, C: $i] : ((((((~environment(A)) | (~in_environment(A, B))) | (~subpopulation(C, A, B))) | (~greater(cardinality_at_time(C, B), zero))) | (~decreases(cardinality_at_time(C, B)))) | greater(zero, growth_rate(C, B)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_growth_rate_42')).
% 0.12/0.44 tff(202,plain,
% 0.12/0.44 (![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(zero, growth_rate(C, B)) | (~decreases(cardinality_at_time(C, B))))),
% 0.12/0.44 inference(modus_ponens,[status(thm)],[201, 200])).
% 0.12/0.44 tff(203,plain,
% 0.12/0.44 (![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(zero, growth_rate(C, B)) | (~decreases(cardinality_at_time(C, B))))),
% 0.12/0.44 inference(modus_ponens,[status(thm)],[202, 198])).
% 0.12/0.44 tff(204,plain,(
% 0.12/0.44 ![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(zero, growth_rate(C, B)) | (~decreases(cardinality_at_time(C, B))))),
% 0.12/0.44 inference(skolemize,[status(sab)],[203])).
% 0.12/0.44 tff(205,plain,
% 0.12/0.44 (![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(zero, growth_rate(C, B)) | (~decreases(cardinality_at_time(C, B))))),
% 0.12/0.44 inference(modus_ponens,[status(thm)],[204, 197])).
% 0.12/0.44 tff(206,plain,
% 0.12/0.44 (((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(zero, growth_rate(C, B)) | (~decreases(cardinality_at_time(C, B))))) | (greater(zero, growth_rate(first_movers, sk2)) | (~environment(sk1)) | (~subpopulation(first_movers, sk1, sk2)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~decreases(cardinality_at_time(first_movers, sk2))))) <=> ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(zero, growth_rate(C, B)) | (~decreases(cardinality_at_time(C, B))))) | greater(zero, growth_rate(first_movers, sk2)) | (~environment(sk1)) | (~subpopulation(first_movers, sk1, sk2)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~decreases(cardinality_at_time(first_movers, sk2))))),
% 0.12/0.44 inference(rewrite,[status(thm)],[])).
% 0.12/0.44 tff(207,plain,
% 0.12/0.44 (((~environment(sk1)) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~subpopulation(first_movers, sk1, sk2)) | (~in_environment(sk1, sk2)) | greater(zero, growth_rate(first_movers, sk2)) | (~decreases(cardinality_at_time(first_movers, sk2)))) <=> (greater(zero, growth_rate(first_movers, sk2)) | (~environment(sk1)) | (~subpopulation(first_movers, sk1, sk2)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~decreases(cardinality_at_time(first_movers, sk2))))),
% 0.12/0.44 inference(rewrite,[status(thm)],[])).
% 0.12/0.44 tff(208,plain,
% 0.12/0.44 (((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(zero, growth_rate(C, B)) | (~decreases(cardinality_at_time(C, B))))) | ((~environment(sk1)) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~subpopulation(first_movers, sk1, sk2)) | (~in_environment(sk1, sk2)) | greater(zero, growth_rate(first_movers, sk2)) | (~decreases(cardinality_at_time(first_movers, sk2))))) <=> ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(zero, growth_rate(C, B)) | (~decreases(cardinality_at_time(C, B))))) | (greater(zero, growth_rate(first_movers, sk2)) | (~environment(sk1)) | (~subpopulation(first_movers, sk1, sk2)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~decreases(cardinality_at_time(first_movers, sk2)))))),
% 0.12/0.44 inference(monotonicity,[status(thm)],[207])).
% 0.12/0.44 tff(209,plain,
% 0.12/0.44 (((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(zero, growth_rate(C, B)) | (~decreases(cardinality_at_time(C, B))))) | ((~environment(sk1)) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~subpopulation(first_movers, sk1, sk2)) | (~in_environment(sk1, sk2)) | greater(zero, growth_rate(first_movers, sk2)) | (~decreases(cardinality_at_time(first_movers, sk2))))) <=> ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(zero, growth_rate(C, B)) | (~decreases(cardinality_at_time(C, B))))) | greater(zero, growth_rate(first_movers, sk2)) | (~environment(sk1)) | (~subpopulation(first_movers, sk1, sk2)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~decreases(cardinality_at_time(first_movers, sk2))))),
% 0.12/0.44 inference(transitivity,[status(thm)],[208, 206])).
% 0.12/0.44 tff(210,plain,
% 0.12/0.44 ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(zero, growth_rate(C, B)) | (~decreases(cardinality_at_time(C, B))))) | ((~environment(sk1)) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~subpopulation(first_movers, sk1, sk2)) | (~in_environment(sk1, sk2)) | greater(zero, growth_rate(first_movers, sk2)) | (~decreases(cardinality_at_time(first_movers, sk2))))),
% 0.12/0.44 inference(quant_inst,[status(thm)],[])).
% 0.12/0.44 tff(211,plain,
% 0.12/0.44 ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(zero, growth_rate(C, B)) | (~decreases(cardinality_at_time(C, B))))) | greater(zero, growth_rate(first_movers, sk2)) | (~environment(sk1)) | (~subpopulation(first_movers, sk1, sk2)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~decreases(cardinality_at_time(first_movers, sk2)))),
% 0.12/0.44 inference(modus_ponens,[status(thm)],[210, 209])).
% 0.12/0.44 tff(212,plain,
% 0.12/0.44 (greater(zero, growth_rate(first_movers, sk2)) | (~decreases(cardinality_at_time(first_movers, sk2)))),
% 0.12/0.44 inference(unit_resolution,[status(thm)],[211, 205, 8, 39, 22, 177])).
% 0.12/0.44 tff(213,plain,
% 0.12/0.44 (greater(zero, growth_rate(first_movers, sk2))),
% 0.12/0.44 inference(unit_resolution,[status(thm)],[212, 195])).
% 0.12/0.44 tff(214,plain,
% 0.12/0.44 (((~greater(growth_rate(efficient_producers, sk2), zero)) | (~greater(zero, growth_rate(first_movers, sk2)))) <=> ((~greater(growth_rate(efficient_producers, sk2), zero)) | (~greater(zero, growth_rate(first_movers, sk2))))),
% 0.12/0.44 inference(rewrite,[status(thm)],[])).
% 0.12/0.44 tff(215,axiom,((~greater(growth_rate(efficient_producers, sk2), zero)) | (~greater(zero, growth_rate(first_movers, sk2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_l7_52')).
% 0.12/0.44 tff(216,plain,
% 0.12/0.44 ((~greater(growth_rate(efficient_producers, sk2), zero)) | (~greater(zero, growth_rate(first_movers, sk2)))),
% 0.12/0.44 inference(modus_ponens,[status(thm)],[215, 214])).
% 0.12/0.44 tff(217,plain,
% 0.12/0.44 ((~greater(growth_rate(efficient_producers, sk2), zero)) | (~greater(zero, growth_rate(first_movers, sk2)))),
% 0.12/0.44 inference(modus_ponens,[status(thm)],[216, 214])).
% 0.12/0.44 tff(218,plain,
% 0.12/0.44 ((~greater(growth_rate(efficient_producers, sk2), zero)) | (~greater(zero, growth_rate(first_movers, sk2)))),
% 0.12/0.44 inference(modus_ponens,[status(thm)],[217, 214])).
% 0.12/0.44 tff(219,plain,
% 0.12/0.44 ((~greater(growth_rate(efficient_producers, sk2), zero)) | (~greater(zero, growth_rate(first_movers, sk2)))),
% 0.12/0.44 inference(modus_ponens,[status(thm)],[218, 214])).
% 0.12/0.44 tff(220,plain,
% 0.12/0.44 ((~greater(growth_rate(efficient_producers, sk2), zero)) | (~greater(zero, growth_rate(first_movers, sk2)))),
% 0.12/0.44 inference(modus_ponens,[status(thm)],[219, 214])).
% 0.12/0.44 tff(221,plain,
% 0.12/0.44 (~greater(growth_rate(efficient_producers, sk2), zero)),
% 0.12/0.44 inference(unit_resolution,[status(thm)],[220, 213])).
% 0.12/0.44 tff(222,plain,
% 0.12/0.44 (^[B: $i, A: $i, C: $i] : refl(((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(growth_rate(C, B), zero) | (~increases(cardinality_at_time(C, B)))) <=> ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(growth_rate(C, B), zero) | (~increases(cardinality_at_time(C, B)))))),
% 0.12/0.44 inference(bind,[status(th)],[])).
% 0.12/0.44 tff(223,plain,
% 0.12/0.44 (![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(growth_rate(C, B), zero) | (~increases(cardinality_at_time(C, B)))) <=> ![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(growth_rate(C, B), zero) | (~increases(cardinality_at_time(C, B))))),
% 0.12/0.44 inference(quant_intro,[status(thm)],[222])).
% 0.12/0.44 tff(224,plain,
% 0.12/0.44 (![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(growth_rate(C, B), zero) | (~increases(cardinality_at_time(C, B)))) <=> ![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(growth_rate(C, B), zero) | (~increases(cardinality_at_time(C, B))))),
% 0.12/0.44 inference(rewrite,[status(thm)],[])).
% 0.12/0.44 tff(225,plain,
% 0.12/0.44 (^[B: $i, A: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite((((~environment(A)) | (~in_environment(A, B))) | (~subpopulation(C, A, B))) <=> ((~environment(A)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))), (((((~environment(A)) | (~in_environment(A, B))) | (~subpopulation(C, A, B))) | (~greater(cardinality_at_time(C, B), zero))) <=> (((~environment(A)) | (~subpopulation(C, A, B)) | (~in_environment(A, B))) | (~greater(cardinality_at_time(C, B), zero))))), rewrite((((~environment(A)) | (~subpopulation(C, A, B)) | (~in_environment(A, B))) | (~greater(cardinality_at_time(C, B), zero))) <=> ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)))), (((((~environment(A)) | (~in_environment(A, B))) | (~subpopulation(C, A, B))) | (~greater(cardinality_at_time(C, B), zero))) <=> ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B))))), ((((((~environment(A)) | (~in_environment(A, B))) | (~subpopulation(C, A, B))) | (~greater(cardinality_at_time(C, B), zero))) | (~increases(cardinality_at_time(C, B)))) <=> (((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B))) | (~increases(cardinality_at_time(C, B)))))), rewrite((((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B))) | (~increases(cardinality_at_time(C, B)))) <=> ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | (~increases(cardinality_at_time(C, B))))), ((((((~environment(A)) | (~in_environment(A, B))) | (~subpopulation(C, A, B))) | (~greater(cardinality_at_time(C, B), zero))) | (~increases(cardinality_at_time(C, B)))) <=> ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | (~increases(cardinality_at_time(C, B)))))), (((((((~environment(A)) | (~in_environment(A, B))) | (~subpopulation(C, A, B))) | (~greater(cardinality_at_time(C, B), zero))) | (~increases(cardinality_at_time(C, B)))) | greater(growth_rate(C, B), zero)) <=> (((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | (~increases(cardinality_at_time(C, B)))) | greater(growth_rate(C, B), zero)))), rewrite((((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | (~increases(cardinality_at_time(C, B)))) | greater(growth_rate(C, B), zero)) <=> ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(growth_rate(C, B), zero) | (~increases(cardinality_at_time(C, B))))), (((((((~environment(A)) | (~in_environment(A, B))) | (~subpopulation(C, A, B))) | (~greater(cardinality_at_time(C, B), zero))) | (~increases(cardinality_at_time(C, B)))) | greater(growth_rate(C, B), zero)) <=> ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(growth_rate(C, B), zero) | (~increases(cardinality_at_time(C, B))))))),
% 0.12/0.45 inference(bind,[status(th)],[])).
% 0.12/0.45 tff(226,plain,
% 0.12/0.45 (![B: $i, A: $i, C: $i] : ((((((~environment(A)) | (~in_environment(A, B))) | (~subpopulation(C, A, B))) | (~greater(cardinality_at_time(C, B), zero))) | (~increases(cardinality_at_time(C, B)))) | greater(growth_rate(C, B), zero)) <=> ![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(growth_rate(C, B), zero) | (~increases(cardinality_at_time(C, B))))),
% 0.12/0.45 inference(quant_intro,[status(thm)],[225])).
% 0.12/0.45 tff(227,axiom,(![B: $i, A: $i, C: $i] : ((((((~environment(A)) | (~in_environment(A, B))) | (~subpopulation(C, A, B))) | (~greater(cardinality_at_time(C, B), zero))) | (~increases(cardinality_at_time(C, B)))) | greater(growth_rate(C, B), zero))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_growth_rate_41')).
% 0.12/0.45 tff(228,plain,
% 0.12/0.45 (![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(growth_rate(C, B), zero) | (~increases(cardinality_at_time(C, B))))),
% 0.12/0.45 inference(modus_ponens,[status(thm)],[227, 226])).
% 0.12/0.45 tff(229,plain,
% 0.12/0.45 (![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(growth_rate(C, B), zero) | (~increases(cardinality_at_time(C, B))))),
% 0.12/0.45 inference(modus_ponens,[status(thm)],[228, 224])).
% 0.12/0.45 tff(230,plain,(
% 0.12/0.45 ![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(growth_rate(C, B), zero) | (~increases(cardinality_at_time(C, B))))),
% 0.12/0.45 inference(skolemize,[status(sab)],[229])).
% 0.12/0.45 tff(231,plain,
% 0.12/0.45 (![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(growth_rate(C, B), zero) | (~increases(cardinality_at_time(C, B))))),
% 0.12/0.45 inference(modus_ponens,[status(thm)],[230, 223])).
% 0.12/0.45 tff(232,plain,
% 0.12/0.45 (((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(growth_rate(C, B), zero) | (~increases(cardinality_at_time(C, B))))) | (greater(growth_rate(efficient_producers, sk2), zero) | (~environment(sk1)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~increases(cardinality_at_time(efficient_producers, sk2))))) <=> ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(growth_rate(C, B), zero) | (~increases(cardinality_at_time(C, B))))) | greater(growth_rate(efficient_producers, sk2), zero) | (~environment(sk1)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~increases(cardinality_at_time(efficient_producers, sk2))))),
% 0.12/0.45 inference(rewrite,[status(thm)],[])).
% 0.12/0.45 tff(233,plain,
% 0.12/0.45 (((~environment(sk1)) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~in_environment(sk1, sk2)) | greater(growth_rate(efficient_producers, sk2), zero) | (~increases(cardinality_at_time(efficient_producers, sk2)))) <=> (greater(growth_rate(efficient_producers, sk2), zero) | (~environment(sk1)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~increases(cardinality_at_time(efficient_producers, sk2))))),
% 0.12/0.45 inference(rewrite,[status(thm)],[])).
% 0.12/0.45 tff(234,plain,
% 0.12/0.45 (((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(growth_rate(C, B), zero) | (~increases(cardinality_at_time(C, B))))) | ((~environment(sk1)) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~in_environment(sk1, sk2)) | greater(growth_rate(efficient_producers, sk2), zero) | (~increases(cardinality_at_time(efficient_producers, sk2))))) <=> ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(growth_rate(C, B), zero) | (~increases(cardinality_at_time(C, B))))) | (greater(growth_rate(efficient_producers, sk2), zero) | (~environment(sk1)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~increases(cardinality_at_time(efficient_producers, sk2)))))),
% 0.12/0.45 inference(monotonicity,[status(thm)],[233])).
% 0.12/0.45 tff(235,plain,
% 0.12/0.45 (((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(growth_rate(C, B), zero) | (~increases(cardinality_at_time(C, B))))) | ((~environment(sk1)) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~in_environment(sk1, sk2)) | greater(growth_rate(efficient_producers, sk2), zero) | (~increases(cardinality_at_time(efficient_producers, sk2))))) <=> ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(growth_rate(C, B), zero) | (~increases(cardinality_at_time(C, B))))) | greater(growth_rate(efficient_producers, sk2), zero) | (~environment(sk1)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~increases(cardinality_at_time(efficient_producers, sk2))))),
% 0.12/0.45 inference(transitivity,[status(thm)],[234, 232])).
% 0.12/0.45 tff(236,plain,
% 0.12/0.45 ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(growth_rate(C, B), zero) | (~increases(cardinality_at_time(C, B))))) | ((~environment(sk1)) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~in_environment(sk1, sk2)) | greater(growth_rate(efficient_producers, sk2), zero) | (~increases(cardinality_at_time(efficient_producers, sk2))))),
% 0.12/0.45 inference(quant_inst,[status(thm)],[])).
% 0.12/0.45 tff(237,plain,
% 0.12/0.45 ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(growth_rate(C, B), zero) | (~increases(cardinality_at_time(C, B))))) | greater(growth_rate(efficient_producers, sk2), zero) | (~environment(sk1)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~increases(cardinality_at_time(efficient_producers, sk2)))),
% 0.12/0.45 inference(modus_ponens,[status(thm)],[236, 235])).
% 0.12/0.45 tff(238,plain,
% 0.12/0.45 (greater(growth_rate(efficient_producers, sk2), zero) | (~increases(cardinality_at_time(efficient_producers, sk2)))),
% 0.12/0.45 inference(unit_resolution,[status(thm)],[237, 231, 8, 119, 22, 102])).
% 0.12/0.45 tff(239,plain,
% 0.12/0.45 (~increases(cardinality_at_time(efficient_producers, sk2))),
% 0.12/0.45 inference(unit_resolution,[status(thm)],[238, 221])).
% 0.12/0.45 tff(240,plain,
% 0.12/0.45 (^[B: $i, C: $i] : refl((increases(C) | constant(C) | increases(B) | (~constant(sum(B, C)))) <=> (increases(C) | constant(C) | increases(B) | (~constant(sum(B, C)))))),
% 0.12/0.45 inference(bind,[status(th)],[])).
% 0.12/0.45 tff(241,plain,
% 0.12/0.45 (![B: $i, C: $i] : (increases(C) | constant(C) | increases(B) | (~constant(sum(B, C)))) <=> ![B: $i, C: $i] : (increases(C) | constant(C) | increases(B) | (~constant(sum(B, C))))),
% 0.12/0.45 inference(quant_intro,[status(thm)],[240])).
% 0.12/0.45 tff(242,plain,
% 0.12/0.45 (![B: $i, C: $i] : (increases(C) | constant(C) | increases(B) | (~constant(sum(B, C)))) <=> ![B: $i, C: $i] : (increases(C) | constant(C) | increases(B) | (~constant(sum(B, C))))),
% 0.12/0.45 inference(rewrite,[status(thm)],[])).
% 0.12/0.45 tff(243,plain,
% 0.12/0.45 (^[B: $i, C: $i] : rewrite((constant(C) | increases(B) | (~constant(sum(B, C))) | increases(C)) <=> (increases(C) | constant(C) | increases(B) | (~constant(sum(B, C)))))),
% 0.12/0.45 inference(bind,[status(th)],[])).
% 0.12/0.45 tff(244,plain,
% 0.12/0.45 (![B: $i, C: $i] : (constant(C) | increases(B) | (~constant(sum(B, C))) | increases(C)) <=> ![B: $i, C: $i] : (increases(C) | constant(C) | increases(B) | (~constant(sum(B, C))))),
% 0.12/0.45 inference(quant_intro,[status(thm)],[243])).
% 0.12/0.45 tff(245,plain,
% 0.12/0.45 (![B: $i, A: $i, C: $i] : (constant(C) | increases(B) | (~constant(sum(B, C))) | increases(C)) <=> ![B: $i, C: $i] : (constant(C) | increases(B) | (~constant(sum(B, C))) | increases(C))),
% 0.12/0.45 inference(elim_unused_vars,[status(thm)],[])).
% 0.12/0.45 tff(246,plain,
% 0.12/0.45 (![B: $i, A: $i, C: $i] : (increases(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C) | constant(C)) <=> ![B: $i, A: $i, C: $i] : (constant(C) | increases(B) | (~constant(sum(B, C))) | increases(C))),
% 0.12/0.45 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.12/0.45 tff(247,plain,
% 0.12/0.45 (![B: $i, A: $i, C: $i] : (increases(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C) | constant(C)) <=> ![B: $i, C: $i] : (constant(C) | increases(B) | (~constant(sum(B, C))) | increases(C))),
% 0.12/0.45 inference(transitivity,[status(thm)],[246, 245])).
% 0.12/0.45 tff(248,plain,
% 0.12/0.45 (![B: $i, A: $i, C: $i] : (increases(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C) | constant(C)) <=> ![B: $i, C: $i] : (increases(C) | constant(C) | increases(B) | (~constant(sum(B, C))))),
% 0.12/0.45 inference(transitivity,[status(thm)],[247, 244])).
% 0.12/0.45 tff(249,plain,
% 0.12/0.45 (^[B: $i, A: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~(A = sum(B, C))) | (~constant(A))) <=> ((~constant(A)) | (~(A = sum(B, C))))), ((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) <=> (((~constant(A)) | (~(A = sum(B, C)))) | constant(C)))), rewrite((((~constant(A)) | (~(A = sum(B, C)))) | constant(C)) <=> ((~constant(A)) | (~(A = sum(B, C))) | constant(C))), ((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) <=> ((~constant(A)) | (~(A = sum(B, C))) | constant(C)))), (((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) | increases(B)) <=> (((~constant(A)) | (~(A = sum(B, C))) | constant(C)) | increases(B)))), rewrite((((~constant(A)) | (~(A = sum(B, C))) | constant(C)) | increases(B)) <=> (increases(B) | (~constant(A)) | (~(A = sum(B, C))) | constant(C))), (((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) | increases(B)) <=> (increases(B) | (~constant(A)) | (~(A = sum(B, C))) | constant(C)))), ((((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) | increases(B)) | increases(C)) <=> ((increases(B) | (~constant(A)) | (~(A = sum(B, C))) | constant(C)) | increases(C)))), rewrite(((increases(B) | (~constant(A)) | (~(A = sum(B, C))) | constant(C)) | increases(C)) <=> (increases(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C) | constant(C))), ((((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) | increases(B)) | increases(C)) <=> (increases(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C) | constant(C))))),
% 0.12/0.45 inference(bind,[status(th)],[])).
% 0.12/0.45 tff(250,plain,
% 0.12/0.45 (![B: $i, A: $i, C: $i] : (((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) | increases(B)) | increases(C)) <=> ![B: $i, A: $i, C: $i] : (increases(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C) | constant(C))),
% 0.12/0.45 inference(quant_intro,[status(thm)],[249])).
% 0.12/0.45 tff(251,plain,
% 0.12/0.45 (![B: $i, A: $i, C: $i] : (((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) | increases(B)) | increases(C)) <=> ![B: $i, C: $i] : (increases(C) | constant(C) | increases(B) | (~constant(sum(B, C))))),
% 0.12/0.45 inference(transitivity,[status(thm)],[250, 248])).
% 0.12/0.45 tff(252,axiom,(![B: $i, A: $i, C: $i] : (((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) | increases(B)) | increases(C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_abc_sum_increase_37')).
% 0.12/0.45 tff(253,plain,
% 0.12/0.45 (![B: $i, C: $i] : (increases(C) | constant(C) | increases(B) | (~constant(sum(B, C))))),
% 0.12/0.45 inference(modus_ponens,[status(thm)],[252, 251])).
% 0.12/0.45 tff(254,plain,
% 0.12/0.45 (![B: $i, C: $i] : (increases(C) | constant(C) | increases(B) | (~constant(sum(B, C))))),
% 0.12/0.45 inference(modus_ponens,[status(thm)],[253, 242])).
% 0.12/0.45 tff(255,plain,(
% 0.12/0.45 ![B: $i, C: $i] : (increases(C) | constant(C) | increases(B) | (~constant(sum(B, C))))),
% 0.12/0.45 inference(skolemize,[status(sab)],[254])).
% 0.12/0.45 tff(256,plain,
% 0.12/0.45 (![B: $i, C: $i] : (increases(C) | constant(C) | increases(B) | (~constant(sum(B, C))))),
% 0.12/0.45 inference(modus_ponens,[status(thm)],[255, 241])).
% 0.12/0.45 tff(257,plain,
% 0.12/0.45 (((~![B: $i, C: $i] : (increases(C) | constant(C) | increases(B) | (~constant(sum(B, C))))) | (increases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))) <=> ((~![B: $i, C: $i] : (increases(C) | constant(C) | increases(B) | (~constant(sum(B, C))))) | increases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))),
% 0.12/0.45 inference(rewrite,[status(thm)],[])).
% 0.12/0.45 tff(258,plain,
% 0.12/0.45 ((increases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | increases(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))))) <=> (increases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))),
% 0.12/0.45 inference(rewrite,[status(thm)],[])).
% 0.12/0.45 tff(259,plain,
% 0.12/0.45 (((~![B: $i, C: $i] : (increases(C) | constant(C) | increases(B) | (~constant(sum(B, C))))) | (increases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | increases(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))) <=> ((~![B: $i, C: $i] : (increases(C) | constant(C) | increases(B) | (~constant(sum(B, C))))) | (increases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))))))),
% 0.12/0.45 inference(monotonicity,[status(thm)],[258])).
% 0.12/0.45 tff(260,plain,
% 0.12/0.45 (((~![B: $i, C: $i] : (increases(C) | constant(C) | increases(B) | (~constant(sum(B, C))))) | (increases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | increases(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))) <=> ((~![B: $i, C: $i] : (increases(C) | constant(C) | increases(B) | (~constant(sum(B, C))))) | increases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))),
% 0.12/0.45 inference(transitivity,[status(thm)],[259, 257])).
% 0.12/0.45 tff(261,plain,
% 0.12/0.45 ((~![B: $i, C: $i] : (increases(C) | constant(C) | increases(B) | (~constant(sum(B, C))))) | (increases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | increases(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))),
% 0.12/0.45 inference(quant_inst,[status(thm)],[])).
% 0.12/0.45 tff(262,plain,
% 0.12/0.45 ((~![B: $i, C: $i] : (increases(C) | constant(C) | increases(B) | (~constant(sum(B, C))))) | increases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))))),
% 0.12/0.45 inference(modus_ponens,[status(thm)],[261, 260])).
% 0.12/0.45 tff(263,plain,
% 0.12/0.45 (increases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))))),
% 0.12/0.45 inference(unit_resolution,[status(thm)],[262, 256])).
% 0.12/0.45 tff(264,plain,
% 0.12/0.45 (increases(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2))),
% 0.12/0.45 inference(unit_resolution,[status(thm)],[263, 68])).
% 0.12/0.45 tff(265,plain,
% 0.12/0.45 (constant(cardinality_at_time(efficient_producers, sk2))),
% 0.12/0.45 inference(unit_resolution,[status(thm)],[264, 239, 1])).
% 0.12/0.45 tff(266,plain,
% 0.12/0.45 (growth_rate(efficient_producers, sk2) = zero),
% 0.12/0.45 inference(unit_resolution,[status(thm)],[136, 265])).
% 0.12/0.45 tff(267,plain,
% 0.12/0.45 (^[B: $i, C: $i] : refl((constant(B) | increases(C) | increases(B) | (~constant(sum(B, C)))) <=> (constant(B) | increases(C) | increases(B) | (~constant(sum(B, C)))))),
% 0.12/0.45 inference(bind,[status(th)],[])).
% 0.12/0.45 tff(268,plain,
% 0.12/0.45 (![B: $i, C: $i] : (constant(B) | increases(C) | increases(B) | (~constant(sum(B, C)))) <=> ![B: $i, C: $i] : (constant(B) | increases(C) | increases(B) | (~constant(sum(B, C))))),
% 0.12/0.45 inference(quant_intro,[status(thm)],[267])).
% 0.12/0.45 tff(269,plain,
% 0.12/0.45 (![B: $i, C: $i] : (constant(B) | increases(C) | increases(B) | (~constant(sum(B, C)))) <=> ![B: $i, C: $i] : (constant(B) | increases(C) | increases(B) | (~constant(sum(B, C))))),
% 0.12/0.45 inference(rewrite,[status(thm)],[])).
% 0.12/0.45 tff(270,plain,
% 0.12/0.45 (^[B: $i, C: $i] : rewrite((increases(C) | increases(B) | constant(B) | (~constant(sum(B, C)))) <=> (constant(B) | increases(C) | increases(B) | (~constant(sum(B, C)))))),
% 0.12/0.45 inference(bind,[status(th)],[])).
% 0.12/0.45 tff(271,plain,
% 0.12/0.45 (![B: $i, C: $i] : (increases(C) | increases(B) | constant(B) | (~constant(sum(B, C)))) <=> ![B: $i, C: $i] : (constant(B) | increases(C) | increases(B) | (~constant(sum(B, C))))),
% 0.12/0.45 inference(quant_intro,[status(thm)],[270])).
% 0.12/0.45 tff(272,plain,
% 0.12/0.45 (![B: $i, A: $i, C: $i] : (increases(C) | increases(B) | constant(B) | (~constant(sum(B, C)))) <=> ![B: $i, C: $i] : (increases(C) | increases(B) | constant(B) | (~constant(sum(B, C))))),
% 0.22/0.45 inference(elim_unused_vars,[status(thm)],[])).
% 0.22/0.45 tff(273,plain,
% 0.22/0.45 (![B: $i, A: $i, C: $i] : (increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C)) <=> ![B: $i, A: $i, C: $i] : (increases(C) | increases(B) | constant(B) | (~constant(sum(B, C))))),
% 0.22/0.45 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.22/0.45 tff(274,plain,
% 0.22/0.45 (![B: $i, A: $i, C: $i] : (increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C)) <=> ![B: $i, C: $i] : (increases(C) | increases(B) | constant(B) | (~constant(sum(B, C))))),
% 0.22/0.45 inference(transitivity,[status(thm)],[273, 272])).
% 0.22/0.45 tff(275,plain,
% 0.22/0.45 (![B: $i, A: $i, C: $i] : (increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C)) <=> ![B: $i, C: $i] : (constant(B) | increases(C) | increases(B) | (~constant(sum(B, C))))),
% 0.22/0.45 inference(transitivity,[status(thm)],[274, 271])).
% 0.22/0.45 tff(276,plain,
% 0.22/0.45 (^[B: $i, A: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~(A = sum(B, C))) | (~constant(A))) <=> ((~constant(A)) | (~(A = sum(B, C))))), ((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) <=> (((~constant(A)) | (~(A = sum(B, C)))) | constant(B)))), rewrite((((~constant(A)) | (~(A = sum(B, C)))) | constant(B)) <=> (constant(B) | (~constant(A)) | (~(A = sum(B, C))))), ((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) <=> (constant(B) | (~constant(A)) | (~(A = sum(B, C)))))), (((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) | increases(B)) <=> ((constant(B) | (~constant(A)) | (~(A = sum(B, C)))) | increases(B)))), rewrite(((constant(B) | (~constant(A)) | (~(A = sum(B, C)))) | increases(B)) <=> (increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))))), (((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) | increases(B)) <=> (increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C)))))), ((((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) | increases(B)) | increases(C)) <=> ((increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C)))) | increases(C)))), rewrite(((increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C)))) | increases(C)) <=> (increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C))), ((((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) | increases(B)) | increases(C)) <=> (increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C))))),
% 0.22/0.46 inference(bind,[status(th)],[])).
% 0.22/0.46 tff(277,plain,
% 0.22/0.46 (![B: $i, A: $i, C: $i] : (((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) | increases(B)) | increases(C)) <=> ![B: $i, A: $i, C: $i] : (increases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C))),
% 0.22/0.46 inference(quant_intro,[status(thm)],[276])).
% 0.22/0.46 tff(278,plain,
% 0.22/0.46 (![B: $i, A: $i, C: $i] : (((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) | increases(B)) | increases(C)) <=> ![B: $i, C: $i] : (constant(B) | increases(C) | increases(B) | (~constant(sum(B, C))))),
% 0.22/0.46 inference(transitivity,[status(thm)],[277, 275])).
% 0.22/0.46 tff(279,axiom,(![B: $i, A: $i, C: $i] : (((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) | increases(B)) | increases(C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_abc_sum_increase_33')).
% 0.22/0.46 tff(280,plain,
% 0.22/0.46 (![B: $i, C: $i] : (constant(B) | increases(C) | increases(B) | (~constant(sum(B, C))))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[279, 278])).
% 0.22/0.46 tff(281,plain,
% 0.22/0.46 (![B: $i, C: $i] : (constant(B) | increases(C) | increases(B) | (~constant(sum(B, C))))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[280, 269])).
% 0.22/0.46 tff(282,plain,(
% 0.22/0.46 ![B: $i, C: $i] : (constant(B) | increases(C) | increases(B) | (~constant(sum(B, C))))),
% 0.22/0.46 inference(skolemize,[status(sab)],[281])).
% 0.22/0.46 tff(283,plain,
% 0.22/0.46 (![B: $i, C: $i] : (constant(B) | increases(C) | increases(B) | (~constant(sum(B, C))))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[282, 268])).
% 0.22/0.46 tff(284,plain,
% 0.22/0.46 (((~![B: $i, C: $i] : (constant(B) | increases(C) | increases(B) | (~constant(sum(B, C))))) | (constant(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | increases(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))) <=> ((~![B: $i, C: $i] : (constant(B) | increases(C) | increases(B) | (~constant(sum(B, C))))) | constant(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | increases(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(285,plain,
% 0.22/0.46 ((~![B: $i, C: $i] : (constant(B) | increases(C) | increases(B) | (~constant(sum(B, C))))) | (constant(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | increases(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(286,plain,
% 0.22/0.46 ((~![B: $i, C: $i] : (constant(B) | increases(C) | increases(B) | (~constant(sum(B, C))))) | constant(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | increases(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[285, 284])).
% 0.22/0.46 tff(287,plain,
% 0.22/0.46 (constant(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | increases(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[286, 283])).
% 0.22/0.46 tff(288,plain,
% 0.22/0.46 (constant(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | increases(cardinality_at_time(first_movers, sk2))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[287, 68])).
% 0.22/0.46 tff(289,plain,
% 0.22/0.46 (constant(cardinality_at_time(first_movers, sk2))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[288, 239, 1])).
% 0.22/0.46 tff(290,plain,
% 0.22/0.46 (growth_rate(first_movers, sk2) = zero),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[184, 289])).
% 0.22/0.46 tff(291,plain,
% 0.22/0.46 ($false),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[192, 290, 266])).
% 0.22/0.46 tff(292,plain,(increases(cardinality_at_time(first_movers, sk2))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.46 tff(293,plain,
% 0.22/0.46 (((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(growth_rate(C, B), zero) | (~increases(cardinality_at_time(C, B))))) | (greater(growth_rate(first_movers, sk2), zero) | (~environment(sk1)) | (~subpopulation(first_movers, sk1, sk2)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~increases(cardinality_at_time(first_movers, sk2))))) <=> ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(growth_rate(C, B), zero) | (~increases(cardinality_at_time(C, B))))) | greater(growth_rate(first_movers, sk2), zero) | (~environment(sk1)) | (~subpopulation(first_movers, sk1, sk2)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~increases(cardinality_at_time(first_movers, sk2))))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(294,plain,
% 0.22/0.46 (((~environment(sk1)) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~subpopulation(first_movers, sk1, sk2)) | (~in_environment(sk1, sk2)) | greater(growth_rate(first_movers, sk2), zero) | (~increases(cardinality_at_time(first_movers, sk2)))) <=> (greater(growth_rate(first_movers, sk2), zero) | (~environment(sk1)) | (~subpopulation(first_movers, sk1, sk2)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~increases(cardinality_at_time(first_movers, sk2))))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(295,plain,
% 0.22/0.46 (((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(growth_rate(C, B), zero) | (~increases(cardinality_at_time(C, B))))) | ((~environment(sk1)) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~subpopulation(first_movers, sk1, sk2)) | (~in_environment(sk1, sk2)) | greater(growth_rate(first_movers, sk2), zero) | (~increases(cardinality_at_time(first_movers, sk2))))) <=> ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(growth_rate(C, B), zero) | (~increases(cardinality_at_time(C, B))))) | (greater(growth_rate(first_movers, sk2), zero) | (~environment(sk1)) | (~subpopulation(first_movers, sk1, sk2)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~increases(cardinality_at_time(first_movers, sk2)))))),
% 0.22/0.46 inference(monotonicity,[status(thm)],[294])).
% 0.22/0.46 tff(296,plain,
% 0.22/0.46 (((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(growth_rate(C, B), zero) | (~increases(cardinality_at_time(C, B))))) | ((~environment(sk1)) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~subpopulation(first_movers, sk1, sk2)) | (~in_environment(sk1, sk2)) | greater(growth_rate(first_movers, sk2), zero) | (~increases(cardinality_at_time(first_movers, sk2))))) <=> ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(growth_rate(C, B), zero) | (~increases(cardinality_at_time(C, B))))) | greater(growth_rate(first_movers, sk2), zero) | (~environment(sk1)) | (~subpopulation(first_movers, sk1, sk2)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~increases(cardinality_at_time(first_movers, sk2))))),
% 0.22/0.46 inference(transitivity,[status(thm)],[295, 293])).
% 0.22/0.46 tff(297,plain,
% 0.22/0.46 ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(growth_rate(C, B), zero) | (~increases(cardinality_at_time(C, B))))) | ((~environment(sk1)) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~subpopulation(first_movers, sk1, sk2)) | (~in_environment(sk1, sk2)) | greater(growth_rate(first_movers, sk2), zero) | (~increases(cardinality_at_time(first_movers, sk2))))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(298,plain,
% 0.22/0.46 ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(growth_rate(C, B), zero) | (~increases(cardinality_at_time(C, B))))) | greater(growth_rate(first_movers, sk2), zero) | (~environment(sk1)) | (~subpopulation(first_movers, sk1, sk2)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(first_movers, sk2), zero)) | (~increases(cardinality_at_time(first_movers, sk2)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[297, 296])).
% 0.22/0.46 tff(299,plain,
% 0.22/0.46 (greater(growth_rate(first_movers, sk2), zero) | (~increases(cardinality_at_time(first_movers, sk2)))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[298, 231, 8, 39, 22, 177])).
% 0.22/0.46 tff(300,plain,
% 0.22/0.46 (greater(growth_rate(first_movers, sk2), zero)),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[299, 292])).
% 0.22/0.46 tff(301,plain,
% 0.22/0.46 (((~greater(growth_rate(first_movers, sk2), zero)) | (~greater(zero, growth_rate(efficient_producers, sk2)))) <=> ((~greater(growth_rate(first_movers, sk2), zero)) | (~greater(zero, growth_rate(efficient_producers, sk2))))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(302,axiom,((~greater(growth_rate(first_movers, sk2), zero)) | (~greater(zero, growth_rate(efficient_producers, sk2)))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','prove_l7_51')).
% 0.22/0.46 tff(303,plain,
% 0.22/0.46 ((~greater(growth_rate(first_movers, sk2), zero)) | (~greater(zero, growth_rate(efficient_producers, sk2)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[302, 301])).
% 0.22/0.46 tff(304,plain,
% 0.22/0.46 ((~greater(growth_rate(first_movers, sk2), zero)) | (~greater(zero, growth_rate(efficient_producers, sk2)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[303, 301])).
% 0.22/0.46 tff(305,plain,
% 0.22/0.46 ((~greater(growth_rate(first_movers, sk2), zero)) | (~greater(zero, growth_rate(efficient_producers, sk2)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[304, 301])).
% 0.22/0.46 tff(306,plain,
% 0.22/0.46 ((~greater(growth_rate(first_movers, sk2), zero)) | (~greater(zero, growth_rate(efficient_producers, sk2)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[305, 301])).
% 0.22/0.46 tff(307,plain,
% 0.22/0.46 ((~greater(growth_rate(first_movers, sk2), zero)) | (~greater(zero, growth_rate(efficient_producers, sk2)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[306, 301])).
% 0.22/0.46 tff(308,plain,
% 0.22/0.46 (~greater(zero, growth_rate(efficient_producers, sk2))),
% 0.22/0.46 inference(unit_resolution,[status(thm)],[307, 300])).
% 0.22/0.46 tff(309,plain,
% 0.22/0.46 (((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(zero, growth_rate(C, B)) | (~decreases(cardinality_at_time(C, B))))) | (greater(zero, growth_rate(efficient_producers, sk2)) | (~environment(sk1)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~decreases(cardinality_at_time(efficient_producers, sk2))))) <=> ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(zero, growth_rate(C, B)) | (~decreases(cardinality_at_time(C, B))))) | greater(zero, growth_rate(efficient_producers, sk2)) | (~environment(sk1)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~decreases(cardinality_at_time(efficient_producers, sk2))))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(310,plain,
% 0.22/0.46 (((~environment(sk1)) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~in_environment(sk1, sk2)) | greater(zero, growth_rate(efficient_producers, sk2)) | (~decreases(cardinality_at_time(efficient_producers, sk2)))) <=> (greater(zero, growth_rate(efficient_producers, sk2)) | (~environment(sk1)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~decreases(cardinality_at_time(efficient_producers, sk2))))),
% 0.22/0.46 inference(rewrite,[status(thm)],[])).
% 0.22/0.46 tff(311,plain,
% 0.22/0.46 (((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(zero, growth_rate(C, B)) | (~decreases(cardinality_at_time(C, B))))) | ((~environment(sk1)) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~in_environment(sk1, sk2)) | greater(zero, growth_rate(efficient_producers, sk2)) | (~decreases(cardinality_at_time(efficient_producers, sk2))))) <=> ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(zero, growth_rate(C, B)) | (~decreases(cardinality_at_time(C, B))))) | (greater(zero, growth_rate(efficient_producers, sk2)) | (~environment(sk1)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~decreases(cardinality_at_time(efficient_producers, sk2)))))),
% 0.22/0.46 inference(monotonicity,[status(thm)],[310])).
% 0.22/0.46 tff(312,plain,
% 0.22/0.46 (((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(zero, growth_rate(C, B)) | (~decreases(cardinality_at_time(C, B))))) | ((~environment(sk1)) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~in_environment(sk1, sk2)) | greater(zero, growth_rate(efficient_producers, sk2)) | (~decreases(cardinality_at_time(efficient_producers, sk2))))) <=> ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(zero, growth_rate(C, B)) | (~decreases(cardinality_at_time(C, B))))) | greater(zero, growth_rate(efficient_producers, sk2)) | (~environment(sk1)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~decreases(cardinality_at_time(efficient_producers, sk2))))),
% 0.22/0.46 inference(transitivity,[status(thm)],[311, 309])).
% 0.22/0.46 tff(313,plain,
% 0.22/0.46 ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(zero, growth_rate(C, B)) | (~decreases(cardinality_at_time(C, B))))) | ((~environment(sk1)) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~in_environment(sk1, sk2)) | greater(zero, growth_rate(efficient_producers, sk2)) | (~decreases(cardinality_at_time(efficient_producers, sk2))))),
% 0.22/0.46 inference(quant_inst,[status(thm)],[])).
% 0.22/0.46 tff(314,plain,
% 0.22/0.46 ((~![B: $i, A: $i, C: $i] : ((~environment(A)) | (~greater(cardinality_at_time(C, B), zero)) | (~subpopulation(C, A, B)) | (~in_environment(A, B)) | greater(zero, growth_rate(C, B)) | (~decreases(cardinality_at_time(C, B))))) | greater(zero, growth_rate(efficient_producers, sk2)) | (~environment(sk1)) | (~subpopulation(efficient_producers, sk1, sk2)) | (~in_environment(sk1, sk2)) | (~greater(cardinality_at_time(efficient_producers, sk2), zero)) | (~decreases(cardinality_at_time(efficient_producers, sk2)))),
% 0.22/0.46 inference(modus_ponens,[status(thm)],[313, 312])).
% 0.22/0.46 tff(315,plain,
% 0.22/0.46 (greater(zero, growth_rate(efficient_producers, sk2)) | (~decreases(cardinality_at_time(efficient_producers, sk2)))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[314, 205, 8, 119, 22, 102])).
% 0.22/0.47 tff(316,plain,
% 0.22/0.47 (~decreases(cardinality_at_time(efficient_producers, sk2))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[315, 308])).
% 0.22/0.47 tff(317,assumption,(~constant(cardinality_at_time(first_movers, sk2))), introduced(assumption)).
% 0.22/0.47 tff(318,plain,
% 0.22/0.47 (^[B: $i, C: $i] : refl((constant(B) | increases(C) | decreases(C) | (~constant(sum(B, C)))) <=> (constant(B) | increases(C) | decreases(C) | (~constant(sum(B, C)))))),
% 0.22/0.47 inference(bind,[status(th)],[])).
% 0.22/0.47 tff(319,plain,
% 0.22/0.47 (![B: $i, C: $i] : (constant(B) | increases(C) | decreases(C) | (~constant(sum(B, C)))) <=> ![B: $i, C: $i] : (constant(B) | increases(C) | decreases(C) | (~constant(sum(B, C))))),
% 0.22/0.47 inference(quant_intro,[status(thm)],[318])).
% 0.22/0.47 tff(320,plain,
% 0.22/0.47 (![B: $i, C: $i] : (constant(B) | increases(C) | decreases(C) | (~constant(sum(B, C)))) <=> ![B: $i, C: $i] : (constant(B) | increases(C) | decreases(C) | (~constant(sum(B, C))))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(321,plain,
% 0.22/0.47 (^[B: $i, C: $i] : rewrite((decreases(C) | constant(B) | (~constant(sum(B, C))) | increases(C)) <=> (constant(B) | increases(C) | decreases(C) | (~constant(sum(B, C)))))),
% 0.22/0.47 inference(bind,[status(th)],[])).
% 0.22/0.47 tff(322,plain,
% 0.22/0.47 (![B: $i, C: $i] : (decreases(C) | constant(B) | (~constant(sum(B, C))) | increases(C)) <=> ![B: $i, C: $i] : (constant(B) | increases(C) | decreases(C) | (~constant(sum(B, C))))),
% 0.22/0.47 inference(quant_intro,[status(thm)],[321])).
% 0.22/0.47 tff(323,plain,
% 0.22/0.47 (![B: $i, A: $i, C: $i] : (decreases(C) | constant(B) | (~constant(sum(B, C))) | increases(C)) <=> ![B: $i, C: $i] : (decreases(C) | constant(B) | (~constant(sum(B, C))) | increases(C))),
% 0.22/0.47 inference(elim_unused_vars,[status(thm)],[])).
% 0.22/0.47 tff(324,plain,
% 0.22/0.47 (![B: $i, A: $i, C: $i] : (constant(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C) | decreases(C)) <=> ![B: $i, A: $i, C: $i] : (decreases(C) | constant(B) | (~constant(sum(B, C))) | increases(C))),
% 0.22/0.47 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.22/0.47 tff(325,plain,
% 0.22/0.47 (![B: $i, A: $i, C: $i] : (constant(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C) | decreases(C)) <=> ![B: $i, C: $i] : (decreases(C) | constant(B) | (~constant(sum(B, C))) | increases(C))),
% 0.22/0.47 inference(transitivity,[status(thm)],[324, 323])).
% 0.22/0.47 tff(326,plain,
% 0.22/0.47 (![B: $i, A: $i, C: $i] : (constant(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C) | decreases(C)) <=> ![B: $i, C: $i] : (constant(B) | increases(C) | decreases(C) | (~constant(sum(B, C))))),
% 0.22/0.47 inference(transitivity,[status(thm)],[325, 322])).
% 0.22/0.47 tff(327,plain,
% 0.22/0.47 (^[B: $i, A: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~(A = sum(B, C))) | (~constant(A))) <=> ((~constant(A)) | (~(A = sum(B, C))))), ((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) <=> (((~constant(A)) | (~(A = sum(B, C)))) | constant(B)))), rewrite((((~constant(A)) | (~(A = sum(B, C)))) | constant(B)) <=> (constant(B) | (~constant(A)) | (~(A = sum(B, C))))), ((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) <=> (constant(B) | (~constant(A)) | (~(A = sum(B, C)))))), (((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) | decreases(C)) <=> ((constant(B) | (~constant(A)) | (~(A = sum(B, C)))) | decreases(C)))), rewrite(((constant(B) | (~constant(A)) | (~(A = sum(B, C)))) | decreases(C)) <=> (constant(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C))), (((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) | decreases(C)) <=> (constant(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C)))), ((((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) | decreases(C)) | increases(C)) <=> ((constant(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C)) | increases(C)))), rewrite(((constant(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C)) | increases(C)) <=> (constant(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C) | decreases(C))), ((((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) | decreases(C)) | increases(C)) <=> (constant(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C) | decreases(C))))),
% 0.22/0.47 inference(bind,[status(th)],[])).
% 0.22/0.47 tff(328,plain,
% 0.22/0.47 (![B: $i, A: $i, C: $i] : (((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) | decreases(C)) | increases(C)) <=> ![B: $i, A: $i, C: $i] : (constant(B) | (~constant(A)) | (~(A = sum(B, C))) | increases(C) | decreases(C))),
% 0.22/0.47 inference(quant_intro,[status(thm)],[327])).
% 0.22/0.47 tff(329,plain,
% 0.22/0.47 (![B: $i, A: $i, C: $i] : (((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) | decreases(C)) | increases(C)) <=> ![B: $i, C: $i] : (constant(B) | increases(C) | decreases(C) | (~constant(sum(B, C))))),
% 0.22/0.47 inference(transitivity,[status(thm)],[328, 326])).
% 0.22/0.47 tff(330,axiom,(![B: $i, A: $i, C: $i] : (((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) | decreases(C)) | increases(C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_abc_sum_increase_35')).
% 0.22/0.47 tff(331,plain,
% 0.22/0.47 (![B: $i, C: $i] : (constant(B) | increases(C) | decreases(C) | (~constant(sum(B, C))))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[330, 329])).
% 0.22/0.47 tff(332,plain,
% 0.22/0.47 (![B: $i, C: $i] : (constant(B) | increases(C) | decreases(C) | (~constant(sum(B, C))))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[331, 320])).
% 0.22/0.47 tff(333,plain,(
% 0.22/0.47 ![B: $i, C: $i] : (constant(B) | increases(C) | decreases(C) | (~constant(sum(B, C))))),
% 0.22/0.47 inference(skolemize,[status(sab)],[332])).
% 0.22/0.47 tff(334,plain,
% 0.22/0.47 (![B: $i, C: $i] : (constant(B) | increases(C) | decreases(C) | (~constant(sum(B, C))))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[333, 319])).
% 0.22/0.47 tff(335,plain,
% 0.22/0.47 (((~![B: $i, C: $i] : (constant(B) | increases(C) | decreases(C) | (~constant(sum(B, C))))) | (constant(cardinality_at_time(first_movers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))) <=> ((~![B: $i, C: $i] : (constant(B) | increases(C) | decreases(C) | (~constant(sum(B, C))))) | constant(cardinality_at_time(first_movers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(336,plain,
% 0.22/0.47 ((constant(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))))) <=> (constant(cardinality_at_time(first_movers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(337,plain,
% 0.22/0.47 (((~![B: $i, C: $i] : (constant(B) | increases(C) | decreases(C) | (~constant(sum(B, C))))) | (constant(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))) <=> ((~![B: $i, C: $i] : (constant(B) | increases(C) | decreases(C) | (~constant(sum(B, C))))) | (constant(cardinality_at_time(first_movers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))))))),
% 0.22/0.47 inference(monotonicity,[status(thm)],[336])).
% 0.22/0.47 tff(338,plain,
% 0.22/0.47 (((~![B: $i, C: $i] : (constant(B) | increases(C) | decreases(C) | (~constant(sum(B, C))))) | (constant(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))) <=> ((~![B: $i, C: $i] : (constant(B) | increases(C) | decreases(C) | (~constant(sum(B, C))))) | constant(cardinality_at_time(first_movers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))),
% 0.22/0.47 inference(transitivity,[status(thm)],[337, 335])).
% 0.22/0.47 tff(339,plain,
% 0.22/0.47 ((~![B: $i, C: $i] : (constant(B) | increases(C) | decreases(C) | (~constant(sum(B, C))))) | (constant(cardinality_at_time(first_movers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))),
% 0.22/0.47 inference(quant_inst,[status(thm)],[])).
% 0.22/0.47 tff(340,plain,
% 0.22/0.47 ((~![B: $i, C: $i] : (constant(B) | increases(C) | decreases(C) | (~constant(sum(B, C))))) | constant(cardinality_at_time(first_movers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[339, 338])).
% 0.22/0.47 tff(341,plain,
% 0.22/0.47 (constant(cardinality_at_time(first_movers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[340, 334])).
% 0.22/0.47 tff(342,plain,
% 0.22/0.47 (constant(cardinality_at_time(first_movers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[341, 68])).
% 0.22/0.47 tff(343,plain,
% 0.22/0.47 (increases(cardinality_at_time(efficient_producers, sk2))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[342, 317, 316])).
% 0.22/0.47 tff(344,plain,
% 0.22/0.47 (greater(growth_rate(efficient_producers, sk2), zero)),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[238, 343])).
% 0.22/0.47 tff(345,plain,
% 0.22/0.47 (^[B: $i, C: $i] : refl((constant(B) | decreases(C) | decreases(B) | (~constant(sum(B, C)))) <=> (constant(B) | decreases(C) | decreases(B) | (~constant(sum(B, C)))))),
% 0.22/0.47 inference(bind,[status(th)],[])).
% 0.22/0.47 tff(346,plain,
% 0.22/0.47 (![B: $i, C: $i] : (constant(B) | decreases(C) | decreases(B) | (~constant(sum(B, C)))) <=> ![B: $i, C: $i] : (constant(B) | decreases(C) | decreases(B) | (~constant(sum(B, C))))),
% 0.22/0.47 inference(quant_intro,[status(thm)],[345])).
% 0.22/0.47 tff(347,plain,
% 0.22/0.47 (![B: $i, C: $i] : (constant(B) | decreases(C) | decreases(B) | (~constant(sum(B, C)))) <=> ![B: $i, C: $i] : (constant(B) | decreases(C) | decreases(B) | (~constant(sum(B, C))))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(348,plain,
% 0.22/0.47 (^[B: $i, C: $i] : rewrite((decreases(C) | decreases(B) | constant(B) | (~constant(sum(B, C)))) <=> (constant(B) | decreases(C) | decreases(B) | (~constant(sum(B, C)))))),
% 0.22/0.47 inference(bind,[status(th)],[])).
% 0.22/0.47 tff(349,plain,
% 0.22/0.47 (![B: $i, C: $i] : (decreases(C) | decreases(B) | constant(B) | (~constant(sum(B, C)))) <=> ![B: $i, C: $i] : (constant(B) | decreases(C) | decreases(B) | (~constant(sum(B, C))))),
% 0.22/0.47 inference(quant_intro,[status(thm)],[348])).
% 0.22/0.47 tff(350,plain,
% 0.22/0.47 (![B: $i, A: $i, C: $i] : (decreases(C) | decreases(B) | constant(B) | (~constant(sum(B, C)))) <=> ![B: $i, C: $i] : (decreases(C) | decreases(B) | constant(B) | (~constant(sum(B, C))))),
% 0.22/0.47 inference(elim_unused_vars,[status(thm)],[])).
% 0.22/0.47 tff(351,plain,
% 0.22/0.47 (![B: $i, A: $i, C: $i] : (decreases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C)) <=> ![B: $i, A: $i, C: $i] : (decreases(C) | decreases(B) | constant(B) | (~constant(sum(B, C))))),
% 0.22/0.47 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.22/0.47 tff(352,plain,
% 0.22/0.47 (![B: $i, A: $i, C: $i] : (decreases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C)) <=> ![B: $i, C: $i] : (decreases(C) | decreases(B) | constant(B) | (~constant(sum(B, C))))),
% 0.22/0.47 inference(transitivity,[status(thm)],[351, 350])).
% 0.22/0.47 tff(353,plain,
% 0.22/0.47 (![B: $i, A: $i, C: $i] : (decreases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C)) <=> ![B: $i, C: $i] : (constant(B) | decreases(C) | decreases(B) | (~constant(sum(B, C))))),
% 0.22/0.47 inference(transitivity,[status(thm)],[352, 349])).
% 0.22/0.47 tff(354,plain,
% 0.22/0.47 (^[B: $i, A: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~(A = sum(B, C))) | (~constant(A))) <=> ((~constant(A)) | (~(A = sum(B, C))))), ((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) <=> (((~constant(A)) | (~(A = sum(B, C)))) | constant(B)))), rewrite((((~constant(A)) | (~(A = sum(B, C)))) | constant(B)) <=> (constant(B) | (~constant(A)) | (~(A = sum(B, C))))), ((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) <=> (constant(B) | (~constant(A)) | (~(A = sum(B, C)))))), (((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) | decreases(C)) <=> ((constant(B) | (~constant(A)) | (~(A = sum(B, C)))) | decreases(C)))), rewrite(((constant(B) | (~constant(A)) | (~(A = sum(B, C)))) | decreases(C)) <=> (constant(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C))), (((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) | decreases(C)) <=> (constant(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C)))), ((((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) | decreases(C)) | decreases(B)) <=> ((constant(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C)) | decreases(B)))), rewrite(((constant(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C)) | decreases(B)) <=> (decreases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C))), ((((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) | decreases(C)) | decreases(B)) <=> (decreases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C))))),
% 0.22/0.47 inference(bind,[status(th)],[])).
% 0.22/0.47 tff(355,plain,
% 0.22/0.47 (![B: $i, A: $i, C: $i] : (((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) | decreases(C)) | decreases(B)) <=> ![B: $i, A: $i, C: $i] : (decreases(B) | constant(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C))),
% 0.22/0.47 inference(quant_intro,[status(thm)],[354])).
% 0.22/0.47 tff(356,plain,
% 0.22/0.47 (![B: $i, A: $i, C: $i] : (((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) | decreases(C)) | decreases(B)) <=> ![B: $i, C: $i] : (constant(B) | decreases(C) | decreases(B) | (~constant(sum(B, C))))),
% 0.22/0.47 inference(transitivity,[status(thm)],[355, 353])).
% 0.22/0.47 tff(357,axiom,(![B: $i, A: $i, C: $i] : (((((~(A = sum(B, C))) | (~constant(A))) | constant(B)) | decreases(C)) | decreases(B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_abc_sum_increase_34')).
% 0.22/0.47 tff(358,plain,
% 0.22/0.47 (![B: $i, C: $i] : (constant(B) | decreases(C) | decreases(B) | (~constant(sum(B, C))))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[357, 356])).
% 0.22/0.47 tff(359,plain,
% 0.22/0.47 (![B: $i, C: $i] : (constant(B) | decreases(C) | decreases(B) | (~constant(sum(B, C))))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[358, 347])).
% 0.22/0.47 tff(360,plain,(
% 0.22/0.47 ![B: $i, C: $i] : (constant(B) | decreases(C) | decreases(B) | (~constant(sum(B, C))))),
% 0.22/0.47 inference(skolemize,[status(sab)],[359])).
% 0.22/0.47 tff(361,plain,
% 0.22/0.47 (![B: $i, C: $i] : (constant(B) | decreases(C) | decreases(B) | (~constant(sum(B, C))))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[360, 346])).
% 0.22/0.47 tff(362,plain,
% 0.22/0.47 (((~![B: $i, C: $i] : (constant(B) | decreases(C) | decreases(B) | (~constant(sum(B, C))))) | (constant(cardinality_at_time(first_movers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | decreases(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))) <=> ((~![B: $i, C: $i] : (constant(B) | decreases(C) | decreases(B) | (~constant(sum(B, C))))) | constant(cardinality_at_time(first_movers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | decreases(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(363,plain,
% 0.22/0.47 ((~![B: $i, C: $i] : (constant(B) | decreases(C) | decreases(B) | (~constant(sum(B, C))))) | (constant(cardinality_at_time(first_movers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | decreases(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))),
% 0.22/0.47 inference(quant_inst,[status(thm)],[])).
% 0.22/0.47 tff(364,plain,
% 0.22/0.47 ((~![B: $i, C: $i] : (constant(B) | decreases(C) | decreases(B) | (~constant(sum(B, C))))) | constant(cardinality_at_time(first_movers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | decreases(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[363, 362])).
% 0.22/0.47 tff(365,plain,
% 0.22/0.47 (constant(cardinality_at_time(first_movers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | decreases(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[364, 361])).
% 0.22/0.47 tff(366,plain,
% 0.22/0.47 (constant(cardinality_at_time(first_movers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | decreases(cardinality_at_time(first_movers, sk2))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[365, 68])).
% 0.22/0.47 tff(367,plain,
% 0.22/0.47 (decreases(cardinality_at_time(first_movers, sk2))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[366, 317, 316])).
% 0.22/0.47 tff(368,plain,
% 0.22/0.47 (greater(zero, growth_rate(first_movers, sk2))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[212, 367])).
% 0.22/0.47 tff(369,plain,
% 0.22/0.47 ($false),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[220, 368, 344])).
% 0.22/0.47 tff(370,plain,(constant(cardinality_at_time(first_movers, sk2))), inference(lemma,lemma(discharge,[]))).
% 0.22/0.47 tff(371,plain,
% 0.22/0.47 (growth_rate(first_movers, sk2) = zero),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[184, 370])).
% 0.22/0.47 tff(372,plain,
% 0.22/0.47 (~(growth_rate(efficient_producers, sk2) = zero)),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[192, 371])).
% 0.22/0.47 tff(373,plain,
% 0.22/0.47 (~constant(cardinality_at_time(efficient_producers, sk2))),
% 0.22/0.47 inference(unit_resolution,[status(thm)],[136, 372])).
% 0.22/0.47 tff(374,plain,
% 0.22/0.47 (^[B: $i, C: $i] : refl((decreases(C) | constant(C) | decreases(B) | (~constant(sum(B, C)))) <=> (decreases(C) | constant(C) | decreases(B) | (~constant(sum(B, C)))))),
% 0.22/0.47 inference(bind,[status(th)],[])).
% 0.22/0.47 tff(375,plain,
% 0.22/0.47 (![B: $i, C: $i] : (decreases(C) | constant(C) | decreases(B) | (~constant(sum(B, C)))) <=> ![B: $i, C: $i] : (decreases(C) | constant(C) | decreases(B) | (~constant(sum(B, C))))),
% 0.22/0.47 inference(quant_intro,[status(thm)],[374])).
% 0.22/0.47 tff(376,plain,
% 0.22/0.47 (![B: $i, C: $i] : (decreases(C) | constant(C) | decreases(B) | (~constant(sum(B, C)))) <=> ![B: $i, C: $i] : (decreases(C) | constant(C) | decreases(B) | (~constant(sum(B, C))))),
% 0.22/0.47 inference(rewrite,[status(thm)],[])).
% 0.22/0.47 tff(377,plain,
% 0.22/0.47 (^[B: $i, C: $i] : rewrite((constant(C) | decreases(B) | (~constant(sum(B, C))) | decreases(C)) <=> (decreases(C) | constant(C) | decreases(B) | (~constant(sum(B, C)))))),
% 0.22/0.47 inference(bind,[status(th)],[])).
% 0.22/0.47 tff(378,plain,
% 0.22/0.47 (![B: $i, C: $i] : (constant(C) | decreases(B) | (~constant(sum(B, C))) | decreases(C)) <=> ![B: $i, C: $i] : (decreases(C) | constant(C) | decreases(B) | (~constant(sum(B, C))))),
% 0.22/0.47 inference(quant_intro,[status(thm)],[377])).
% 0.22/0.47 tff(379,plain,
% 0.22/0.47 (![B: $i, A: $i, C: $i] : (constant(C) | decreases(B) | (~constant(sum(B, C))) | decreases(C)) <=> ![B: $i, C: $i] : (constant(C) | decreases(B) | (~constant(sum(B, C))) | decreases(C))),
% 0.22/0.47 inference(elim_unused_vars,[status(thm)],[])).
% 0.22/0.47 tff(380,plain,
% 0.22/0.47 (![B: $i, A: $i, C: $i] : (decreases(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C) | constant(C)) <=> ![B: $i, A: $i, C: $i] : (constant(C) | decreases(B) | (~constant(sum(B, C))) | decreases(C))),
% 0.22/0.47 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.22/0.47 tff(381,plain,
% 0.22/0.47 (![B: $i, A: $i, C: $i] : (decreases(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C) | constant(C)) <=> ![B: $i, C: $i] : (constant(C) | decreases(B) | (~constant(sum(B, C))) | decreases(C))),
% 0.22/0.47 inference(transitivity,[status(thm)],[380, 379])).
% 0.22/0.47 tff(382,plain,
% 0.22/0.47 (![B: $i, A: $i, C: $i] : (decreases(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C) | constant(C)) <=> ![B: $i, C: $i] : (decreases(C) | constant(C) | decreases(B) | (~constant(sum(B, C))))),
% 0.22/0.47 inference(transitivity,[status(thm)],[381, 378])).
% 0.22/0.47 tff(383,plain,
% 0.22/0.47 (^[B: $i, A: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~(A = sum(B, C))) | (~constant(A))) <=> ((~constant(A)) | (~(A = sum(B, C))))), ((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) <=> (((~constant(A)) | (~(A = sum(B, C)))) | constant(C)))), rewrite((((~constant(A)) | (~(A = sum(B, C)))) | constant(C)) <=> ((~constant(A)) | (~(A = sum(B, C))) | constant(C))), ((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) <=> ((~constant(A)) | (~(A = sum(B, C))) | constant(C)))), (((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) | decreases(C)) <=> (((~constant(A)) | (~(A = sum(B, C))) | constant(C)) | decreases(C)))), rewrite((((~constant(A)) | (~(A = sum(B, C))) | constant(C)) | decreases(C)) <=> ((~constant(A)) | (~(A = sum(B, C))) | decreases(C) | constant(C))), (((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) | decreases(C)) <=> ((~constant(A)) | (~(A = sum(B, C))) | decreases(C) | constant(C)))), ((((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) | decreases(C)) | decreases(B)) <=> (((~constant(A)) | (~(A = sum(B, C))) | decreases(C) | constant(C)) | decreases(B)))), rewrite((((~constant(A)) | (~(A = sum(B, C))) | decreases(C) | constant(C)) | decreases(B)) <=> (decreases(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C) | constant(C))), ((((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) | decreases(C)) | decreases(B)) <=> (decreases(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C) | constant(C))))),
% 0.22/0.47 inference(bind,[status(th)],[])).
% 0.22/0.47 tff(384,plain,
% 0.22/0.47 (![B: $i, A: $i, C: $i] : (((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) | decreases(C)) | decreases(B)) <=> ![B: $i, A: $i, C: $i] : (decreases(B) | (~constant(A)) | (~(A = sum(B, C))) | decreases(C) | constant(C))),
% 0.22/0.47 inference(quant_intro,[status(thm)],[383])).
% 0.22/0.47 tff(385,plain,
% 0.22/0.47 (![B: $i, A: $i, C: $i] : (((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) | decreases(C)) | decreases(B)) <=> ![B: $i, C: $i] : (decreases(C) | constant(C) | decreases(B) | (~constant(sum(B, C))))),
% 0.22/0.47 inference(transitivity,[status(thm)],[384, 382])).
% 0.22/0.47 tff(386,axiom,(![B: $i, A: $i, C: $i] : (((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) | decreases(C)) | decreases(B))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_abc_sum_increase_38')).
% 0.22/0.47 tff(387,plain,
% 0.22/0.47 (![B: $i, C: $i] : (decreases(C) | constant(C) | decreases(B) | (~constant(sum(B, C))))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[386, 385])).
% 0.22/0.47 tff(388,plain,
% 0.22/0.47 (![B: $i, C: $i] : (decreases(C) | constant(C) | decreases(B) | (~constant(sum(B, C))))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[387, 376])).
% 0.22/0.47 tff(389,plain,(
% 0.22/0.47 ![B: $i, C: $i] : (decreases(C) | constant(C) | decreases(B) | (~constant(sum(B, C))))),
% 0.22/0.47 inference(skolemize,[status(sab)],[388])).
% 0.22/0.47 tff(390,plain,
% 0.22/0.47 (![B: $i, C: $i] : (decreases(C) | constant(C) | decreases(B) | (~constant(sum(B, C))))),
% 0.22/0.47 inference(modus_ponens,[status(thm)],[389, 375])).
% 0.22/0.47 tff(391,plain,
% 0.22/0.47 (((~![B: $i, C: $i] : (decreases(C) | constant(C) | decreases(B) | (~constant(sum(B, C))))) | (decreases(cardinality_at_time(first_movers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))) <=> ((~![B: $i, C: $i] : (decreases(C) | constant(C) | decreases(B) | (~constant(sum(B, C))))) | decreases(cardinality_at_time(first_movers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(392,plain,
% 0.22/0.48 ((decreases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | decreases(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))))) <=> (decreases(cardinality_at_time(first_movers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(393,plain,
% 0.22/0.48 (((~![B: $i, C: $i] : (decreases(C) | constant(C) | decreases(B) | (~constant(sum(B, C))))) | (decreases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | decreases(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))) <=> ((~![B: $i, C: $i] : (decreases(C) | constant(C) | decreases(B) | (~constant(sum(B, C))))) | (decreases(cardinality_at_time(first_movers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))))))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[392])).
% 0.22/0.48 tff(394,plain,
% 0.22/0.48 (((~![B: $i, C: $i] : (decreases(C) | constant(C) | decreases(B) | (~constant(sum(B, C))))) | (decreases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | decreases(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))) <=> ((~![B: $i, C: $i] : (decreases(C) | constant(C) | decreases(B) | (~constant(sum(B, C))))) | decreases(cardinality_at_time(first_movers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))),
% 0.22/0.48 inference(transitivity,[status(thm)],[393, 391])).
% 0.22/0.48 tff(395,plain,
% 0.22/0.48 ((~![B: $i, C: $i] : (decreases(C) | constant(C) | decreases(B) | (~constant(sum(B, C))))) | (decreases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | decreases(cardinality_at_time(first_movers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))),
% 0.22/0.48 inference(quant_inst,[status(thm)],[])).
% 0.22/0.48 tff(396,plain,
% 0.22/0.48 ((~![B: $i, C: $i] : (decreases(C) | constant(C) | decreases(B) | (~constant(sum(B, C))))) | decreases(cardinality_at_time(first_movers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[395, 394])).
% 0.22/0.48 tff(397,plain,
% 0.22/0.48 (decreases(cardinality_at_time(first_movers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[396, 390])).
% 0.22/0.48 tff(398,plain,
% 0.22/0.48 (decreases(cardinality_at_time(first_movers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[397, 68])).
% 0.22/0.48 tff(399,plain,
% 0.22/0.48 (decreases(cardinality_at_time(first_movers, sk2))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[398, 373, 316])).
% 0.22/0.48 tff(400,plain,
% 0.22/0.48 (greater(zero, growth_rate(first_movers, sk2))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[212, 399])).
% 0.22/0.48 tff(401,plain,
% 0.22/0.48 (^[B: $i, C: $i] : refl((increases(C) | decreases(C) | constant(C) | (~constant(sum(B, C)))) <=> (increases(C) | decreases(C) | constant(C) | (~constant(sum(B, C)))))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(402,plain,
% 0.22/0.48 (![B: $i, C: $i] : (increases(C) | decreases(C) | constant(C) | (~constant(sum(B, C)))) <=> ![B: $i, C: $i] : (increases(C) | decreases(C) | constant(C) | (~constant(sum(B, C))))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[401])).
% 0.22/0.48 tff(403,plain,
% 0.22/0.48 (![B: $i, C: $i] : (increases(C) | decreases(C) | constant(C) | (~constant(sum(B, C)))) <=> ![B: $i, C: $i] : (increases(C) | decreases(C) | constant(C) | (~constant(sum(B, C))))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(404,plain,
% 0.22/0.48 (^[B: $i, C: $i] : rewrite((constant(C) | (~constant(sum(B, C))) | increases(C) | decreases(C)) <=> (increases(C) | decreases(C) | constant(C) | (~constant(sum(B, C)))))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(405,plain,
% 0.22/0.48 (![B: $i, C: $i] : (constant(C) | (~constant(sum(B, C))) | increases(C) | decreases(C)) <=> ![B: $i, C: $i] : (increases(C) | decreases(C) | constant(C) | (~constant(sum(B, C))))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[404])).
% 0.22/0.48 tff(406,plain,
% 0.22/0.48 (![B: $i, A: $i, C: $i] : (constant(C) | (~constant(sum(B, C))) | increases(C) | decreases(C)) <=> ![B: $i, C: $i] : (constant(C) | (~constant(sum(B, C))) | increases(C) | decreases(C))),
% 0.22/0.48 inference(elim_unused_vars,[status(thm)],[])).
% 0.22/0.48 tff(407,plain,
% 0.22/0.48 (![B: $i, A: $i, C: $i] : ((~constant(A)) | (~(A = sum(B, C))) | increases(C) | decreases(C) | constant(C)) <=> ![B: $i, A: $i, C: $i] : (constant(C) | (~constant(sum(B, C))) | increases(C) | decreases(C))),
% 0.22/0.48 inference(destructive_equality_resolution,[status(thm)],[])).
% 0.22/0.48 tff(408,plain,
% 0.22/0.48 (![B: $i, A: $i, C: $i] : ((~constant(A)) | (~(A = sum(B, C))) | increases(C) | decreases(C) | constant(C)) <=> ![B: $i, C: $i] : (constant(C) | (~constant(sum(B, C))) | increases(C) | decreases(C))),
% 0.22/0.48 inference(transitivity,[status(thm)],[407, 406])).
% 0.22/0.48 tff(409,plain,
% 0.22/0.48 (![B: $i, A: $i, C: $i] : ((~constant(A)) | (~(A = sum(B, C))) | increases(C) | decreases(C) | constant(C)) <=> ![B: $i, C: $i] : (increases(C) | decreases(C) | constant(C) | (~constant(sum(B, C))))),
% 0.22/0.48 inference(transitivity,[status(thm)],[408, 405])).
% 0.22/0.48 tff(410,plain,
% 0.22/0.48 (^[B: $i, A: $i, C: $i] : trans(monotonicity(trans(monotonicity(trans(monotonicity(rewrite(((~(A = sum(B, C))) | (~constant(A))) <=> ((~constant(A)) | (~(A = sum(B, C))))), ((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) <=> (((~constant(A)) | (~(A = sum(B, C)))) | constant(C)))), rewrite((((~constant(A)) | (~(A = sum(B, C)))) | constant(C)) <=> ((~constant(A)) | (~(A = sum(B, C))) | constant(C))), ((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) <=> ((~constant(A)) | (~(A = sum(B, C))) | constant(C)))), (((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) | decreases(C)) <=> (((~constant(A)) | (~(A = sum(B, C))) | constant(C)) | decreases(C)))), rewrite((((~constant(A)) | (~(A = sum(B, C))) | constant(C)) | decreases(C)) <=> ((~constant(A)) | (~(A = sum(B, C))) | decreases(C) | constant(C))), (((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) | decreases(C)) <=> ((~constant(A)) | (~(A = sum(B, C))) | decreases(C) | constant(C)))), ((((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) | decreases(C)) | increases(C)) <=> (((~constant(A)) | (~(A = sum(B, C))) | decreases(C) | constant(C)) | increases(C)))), rewrite((((~constant(A)) | (~(A = sum(B, C))) | decreases(C) | constant(C)) | increases(C)) <=> ((~constant(A)) | (~(A = sum(B, C))) | increases(C) | decreases(C) | constant(C))), ((((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) | decreases(C)) | increases(C)) <=> ((~constant(A)) | (~(A = sum(B, C))) | increases(C) | decreases(C) | constant(C))))),
% 0.22/0.48 inference(bind,[status(th)],[])).
% 0.22/0.48 tff(411,plain,
% 0.22/0.48 (![B: $i, A: $i, C: $i] : (((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) | decreases(C)) | increases(C)) <=> ![B: $i, A: $i, C: $i] : ((~constant(A)) | (~(A = sum(B, C))) | increases(C) | decreases(C) | constant(C))),
% 0.22/0.48 inference(quant_intro,[status(thm)],[410])).
% 0.22/0.48 tff(412,plain,
% 0.22/0.48 (![B: $i, A: $i, C: $i] : (((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) | decreases(C)) | increases(C)) <=> ![B: $i, C: $i] : (increases(C) | decreases(C) | constant(C) | (~constant(sum(B, C))))),
% 0.22/0.48 inference(transitivity,[status(thm)],[411, 409])).
% 0.22/0.48 tff(413,axiom,(![B: $i, A: $i, C: $i] : (((((~(A = sum(B, C))) | (~constant(A))) | constant(C)) | decreases(C)) | increases(C))), file('/export/starexec/sandbox2/benchmark/theBenchmark.p','mp_abc_sum_increase_39')).
% 0.22/0.48 tff(414,plain,
% 0.22/0.48 (![B: $i, C: $i] : (increases(C) | decreases(C) | constant(C) | (~constant(sum(B, C))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[413, 412])).
% 0.22/0.48 tff(415,plain,
% 0.22/0.48 (![B: $i, C: $i] : (increases(C) | decreases(C) | constant(C) | (~constant(sum(B, C))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[414, 403])).
% 0.22/0.48 tff(416,plain,(
% 0.22/0.48 ![B: $i, C: $i] : (increases(C) | decreases(C) | constant(C) | (~constant(sum(B, C))))),
% 0.22/0.48 inference(skolemize,[status(sab)],[415])).
% 0.22/0.48 tff(417,plain,
% 0.22/0.48 (![B: $i, C: $i] : (increases(C) | decreases(C) | constant(C) | (~constant(sum(B, C))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[416, 402])).
% 0.22/0.48 tff(418,plain,
% 0.22/0.48 (((~![B: $i, C: $i] : (increases(C) | decreases(C) | constant(C) | (~constant(sum(B, C))))) | (decreases(cardinality_at_time(efficient_producers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))) <=> ((~![B: $i, C: $i] : (increases(C) | decreases(C) | constant(C) | (~constant(sum(B, C))))) | decreases(cardinality_at_time(efficient_producers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(419,plain,
% 0.22/0.48 ((increases(cardinality_at_time(efficient_producers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))))) <=> (decreases(cardinality_at_time(efficient_producers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))),
% 0.22/0.48 inference(rewrite,[status(thm)],[])).
% 0.22/0.48 tff(420,plain,
% 0.22/0.48 (((~![B: $i, C: $i] : (increases(C) | decreases(C) | constant(C) | (~constant(sum(B, C))))) | (increases(cardinality_at_time(efficient_producers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))) <=> ((~![B: $i, C: $i] : (increases(C) | decreases(C) | constant(C) | (~constant(sum(B, C))))) | (decreases(cardinality_at_time(efficient_producers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))))))),
% 0.22/0.48 inference(monotonicity,[status(thm)],[419])).
% 0.22/0.48 tff(421,plain,
% 0.22/0.48 (((~![B: $i, C: $i] : (increases(C) | decreases(C) | constant(C) | (~constant(sum(B, C))))) | (increases(cardinality_at_time(efficient_producers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))) <=> ((~![B: $i, C: $i] : (increases(C) | decreases(C) | constant(C) | (~constant(sum(B, C))))) | decreases(cardinality_at_time(efficient_producers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))),
% 0.22/0.48 inference(transitivity,[status(thm)],[420, 418])).
% 0.22/0.48 tff(422,plain,
% 0.22/0.48 ((~![B: $i, C: $i] : (increases(C) | decreases(C) | constant(C) | (~constant(sum(B, C))))) | (increases(cardinality_at_time(efficient_producers, sk2)) | decreases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2)))))),
% 0.22/0.48 inference(quant_inst,[status(thm)],[])).
% 0.22/0.48 tff(423,plain,
% 0.22/0.48 ((~![B: $i, C: $i] : (increases(C) | decreases(C) | constant(C) | (~constant(sum(B, C))))) | decreases(cardinality_at_time(efficient_producers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))))),
% 0.22/0.48 inference(modus_ponens,[status(thm)],[422, 421])).
% 0.22/0.48 tff(424,plain,
% 0.22/0.48 (decreases(cardinality_at_time(efficient_producers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2)) | (~constant(sum(cardinality_at_time(first_movers, sk2), cardinality_at_time(efficient_producers, sk2))))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[423, 417])).
% 0.22/0.48 tff(425,plain,
% 0.22/0.48 (decreases(cardinality_at_time(efficient_producers, sk2)) | increases(cardinality_at_time(efficient_producers, sk2)) | constant(cardinality_at_time(efficient_producers, sk2))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[424, 68])).
% 0.22/0.48 tff(426,plain,
% 0.22/0.48 (increases(cardinality_at_time(efficient_producers, sk2))),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[425, 373, 316])).
% 0.22/0.48 tff(427,plain,
% 0.22/0.48 (greater(growth_rate(efficient_producers, sk2), zero)),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[238, 426])).
% 0.22/0.48 tff(428,plain,
% 0.22/0.48 ($false),
% 0.22/0.48 inference(unit_resolution,[status(thm)],[220, 427, 400])).
% 0.22/0.48 % SZS output end Proof
% 0.22/0.49 % E exiting
%------------------------------------------------------------------------------